# User contributions

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- 07:21, 27 November 2017 (diff | hist) . . (+33) . . N User:Vipul/Sandbox (Created page with "<math>e^{\pi^2 + \sqrt{2}}</math>") (current)
- 20:55, 5 September 2016 (diff | hist) . . (+43) . . N User:Vipul/sandbox (Created page with "<math>\frac{e^{\pi}}{\sqrt{t^2 + 1}}</math>") (current)
- 23:55, 17 April 2015 (diff | hist) . . (-8) . . Template:Top notice (current)
- 21:07, 29 January 2014
(diff | hist) . .
**(+1,994)** . . N Ring of Gaussian integers (Created page with "{{particular curing}} ==Definition== The '''ring of Gaussian integers''' <math>\mathbb{Z}[i]</math> is defined in the following ways: # It is the subring generated by the [...") (current) - 20:55, 29 January 2014 (diff | hist) . . (+248) . . N Template:Particular curing (Created page with "{{quotation|This article defines a particular commutative unital ring.<br>See all particular commutative unital rings}}<i...") (current)
- 20:54, 29 January 2014
(diff | hist) . .
**(+1,603)** . . Ring of rational integers (current) - 20:38, 29 January 2014 (diff | hist) . . (+191) . . Ring of integers (current)
- 20:37, 29 January 2014
(diff | hist) . .
**(+530)** . . N Ring of rational integers (Created page with "==Definition== The ring <math>\mathbb{Z}</math>, called the '''ring of rational integers''' or sometimes simply the '''ring of integers''', is the ring whose elements are the...") - 20:35, 29 January 2014 (diff | hist) . . (+39) . . N Z (Redirected page to Ring of rational integers) (current)
- 20:34, 29 January 2014 (diff | hist) . . (+56) . . Euclidean domain (→Relation with other properties) (current)
- 20:33, 29 January 2014 (diff | hist) . . (+387) . . Principal ideal domain (→Definition) (current)
- 20:23, 29 January 2014
(diff | hist) . .
**(+783)** . . Bezout domain (→Relation with other properties) (current) - 15:55, 20 July 2013 (diff | hist) . . (-5) . . Principal ideal domain (→Definition)
- 16:10, 18 July 2013 (diff | hist) . . (+406) . . Universally catenary ring (current)
- 16:09, 18 July 2013 (diff | hist) . . (+3) . . Universally catenary ring (→Weaker properties)
- 16:08, 18 July 2013
(diff | hist) . .
**(+683)** . . Universally catenary ring - 16:04, 18 July 2013 (diff | hist) . . (+214) . . Principal ideal domain (→Weaker properties)
- 16:02, 18 July 2013
(diff | hist) . .
**(+1,439)** . . Catenary ring (current) - 15:55, 18 July 2013 (diff | hist) . . (-4) . . Template:Spectrum-determined curing property (current)
- 15:55, 18 July 2013 (diff | hist) . . (-30) . . Jacobson ring (→Definition) (current)
- 15:55, 18 July 2013
(diff | hist) . .
**(-653)** . . Jacobson ring (→Metaproperties) - 15:54, 18 July 2013 (diff | hist) . . (+1) . . Jacobson ring (→Relation with other properties)
- 15:54, 18 July 2013
(diff | hist) . .
**(+1,748)** . . Jacobson ring - 15:47, 18 July 2013 (diff | hist) . . (-43) . . Jacobson ring
- 15:47, 18 July 2013
(diff | hist) . .
**(+1,737)** . . Jacobson ring - 15:39, 18 July 2013 (diff | hist) . . (+2) . . Cohen-Macaulay ring (current)
- 15:37, 18 July 2013
(diff | hist) . .
**(+680)** . . Cohen-Macaulay ring (→Metaproperties) - 15:05, 18 July 2013 (diff | hist) . . (+33) . . Cohen-Macaulay ring (→Conjunction with other properties)
- 05:00, 18 July 2013
(diff | hist) . .
**(+1,125)** . . Integral domain in which any two irreducible factorizations are equal upto ordering and associates (→Relation with other properties) (current) - 04:48, 18 July 2013 (diff | hist) . . (+408) . . Cohen-Macaulay ring (→Relation with other properties)
- 04:43, 18 July 2013
(diff | hist) . .
**(+1,477)** . . Cohen-Macaulay ring (→Relation with other properties) - 04:34, 18 July 2013 (diff | hist) . . (0) . . m Equivalence of definitions of Cohen-Macaulay ring (Vipul moved page Equivalence of definitions of Cohen-Macaulay to Equivalence of definitions of Cohen-Macaulay ring) (current)
- 04:34, 18 July 2013 (diff | hist) . . (+63) . . N Equivalence of definitions of Cohen-Macaulay (Vipul moved page Equivalence of definitions of Cohen-Macaulay to Equivalence of definitions of Cohen-Macaulay ring) (current)
- 04:33, 18 July 2013 (diff | hist) . . (+33) . . N CM ring (Redirected page to Cohen-Macaulay ring) (current)
- 04:32, 18 July 2013 (diff | hist) . . (+449) . . Equidimensional ring (current)
- 04:29, 18 July 2013
(diff | hist) . .
**(+689)** . . Noetherian local ring (current) - 04:23, 18 July 2013 (diff | hist) . . (+328) . . Euclidean domain (→Weaker properties)
- 04:15, 18 July 2013
(diff | hist) . .
**(+1,314)** . . Euclidean domain (→Relation with other properties) - 03:51, 18 July 2013
(diff | hist) . .
**(+2,375)** . . Dedekind domain (→Relation with other properties) (current) - 03:33, 18 July 2013 (diff | hist) . . (+286) . . Principal ideal domain (→Metaproperties)
- 03:29, 18 July 2013 (diff | hist) . . (-72) . . Principal ideal domain (→Relation with other properties)
- 03:22, 18 July 2013
(diff | hist) . .
**(+992)** . . Principal ideal domain (→Definition) - 03:01, 18 July 2013 (diff | hist) . . (0) . . Noetherian ring (current)
- 03:00, 18 July 2013
(diff | hist) . .
**(+699)** . . Noetherian ring (→Metaproperties) - 02:39, 18 July 2013 (diff | hist) . . (-4) . . Template:Curing property (current)
- 02:36, 18 July 2013
(diff | hist) . .
**(-514)** . . Template:Further (Replaced content with "<tt>Further information: {{{1}}}</tt>") (current) - 02:33, 18 July 2013 (diff | hist) . . (+15) . . Noetherian ring
- 02:33, 18 July 2013 (diff | hist) . . (+240) . . Noetherian ring
- 02:28, 18 July 2013 (diff | hist) . . (-1) . . Noetherian ring (→Weaker properties)
- 02:28, 18 July 2013 (diff | hist) . . (-11) . . Noetherian ring (→Weaker properties)
- 02:27, 18 July 2013 (diff | hist) . . (-11) . . Noetherian ring (→Conjunction with other properties)
- 01:59, 4 July 2012
(diff | hist) . .
**(+599)** . . N Formal power series ring (Created page with "==Definition== Let <math>R</math> be a commutative unital ring. The '''formal power series ring''' over <math>R</math> in one variable, denoted <math>Rx</math> if the...") (current) - 01:55, 4 July 2012 (diff | hist) . . (+184) . . Polynomial ring (→Related notions) (current)
- 01:51, 4 July 2012 (diff | hist) . . (+240) . . Laurent polynomial ring (current)
- 01:49, 4 July 2012 (diff | hist) . . (+1) . . Divided polynomial ring (current)
- 01:49, 4 July 2012
(diff | hist) . .
**(+1,505)** . . N Divided polynomial ring (Created page with "==Definition== Let <math>R</math> be a commutative unital ring. The '''divided polynomial ring in one variable''' with indeterminate <math>x</math> over <math>R</math>, a...") - 01:38, 4 July 2012
(diff | hist) . .
**(+755)** . . N Laurent polynomial ring (Created page with "==Definition== Let <math>R</math> be a commutative unital ring. The '''Laurent polynomial ring''' over <math>R</math> with indeterminate <math>x</math> is denoted <math>R...") - 01:35, 4 July 2012 (diff | hist) . . (+242) . . Polynomial ring (→Definition for commutative rings)
- 01:31, 4 July 2012 (diff | hist) . . (+60) . . Ring generated by binomial polynomials (current)
- 01:11, 4 July 2012 (diff | hist) . . (+284) . . Normal domain (current)
- 01:06, 4 July 2012 (diff | hist) . . (-22) . . Principal ideal domain
- 00:08, 19 December 2011 (diff | hist) . . (0) . . Noetherian ring (→Definition)
- 00:01, 19 December 2011 (diff | hist) . . (-11) . . Noetherian ring (→Stronger properties)
- 00:00, 19 December 2011 (diff | hist) . . (0) . . Noetherian ring (→Definition with symbols)
- 17:56, 18 December 2011
(diff | hist) . .
**(+1,438)** . . Primary ideal (→Relation with other properties) (current) - 17:50, 18 December 2011 (diff | hist) . . (+51) . . Radical ideal (→Important ring types) (current)
- 17:48, 18 December 2011
(diff | hist) . .
**(+816)** . . Ideal with prime radical (current) - 17:42, 18 December 2011 (diff | hist) . . (+176) . . Radical ideal (→Important ring types)
- 17:41, 18 December 2011 (diff | hist) . . (+159) . . Radical ideal (→Important ring types)
- 17:39, 18 December 2011
(diff | hist) . .
**(+538)** . . Radical ideal (→Relation with other properties) - 17:36, 18 December 2011
(diff | hist) . .
**(+1,267)** . . Radical ideal - 17:29, 18 December 2011
(diff | hist) . .
**(+691)** . . Radical ideal (→Metaproperties) - 17:24, 18 December 2011 (diff | hist) . . (+302) . . Radical ideal (→Equivalent definitions in tabular format)
- 17:21, 18 December 2011 (diff | hist) . . (+12) . . Primary ideal (→Definition)
- 17:21, 18 December 2011 (diff | hist) . . (+292) . . Primary ideal
- 17:15, 18 December 2011
(diff | hist) . .
**(+1,035)** . . Radical ideal - 17:11, 18 December 2011 (diff | hist) . . (+10) . . Template:Quotient is a (current)
- 17:11, 18 December 2011 (diff | hist) . . (+11) . . Template:Curing-ideal property (current)
- 17:05, 18 December 2011 (diff | hist) . . (+20) . . N Property:Importance rank (Created page with "Has type::Number") (current)
- 17:01, 18 December 2011 (diff | hist) . . (+7) . . Template:Quotation (current)
- 17:00, 18 December 2011 (diff | hist) . . (+18) . . Template:Quotation
- 16:59, 18 December 2011 (diff | hist) . . (-145) . . Template:Basicdef (current)
- 16:57, 18 December 2011 (diff | hist) . . (-339) . . MediaWiki:Sitenotice (Blanked the page) (current)
- 16:57, 18 December 2011 (diff | hist) . . (+4) . . Prime ideal (→Equivalent definitions in tabular format) (current)
- 16:55, 18 December 2011
(diff | hist) . .
**(+1,015)** . . Prime ideal - 21:38, 26 October 2009
(diff | hist) . .
**(+1,415)** . . Normal domain - 21:33, 26 October 2009 (diff | hist) . . (-3) . . Principal ideal domain (→Weaker properties)
- 21:32, 26 October 2009
(diff | hist) . .
**(-537)** . . Principal ideal domain (→Relation with other properties) - 21:31, 26 October 2009
(diff | hist) . .
**(+2,286)** . . Principal ideal domain (→Relation with other properties) - 21:13, 26 October 2009 (diff | hist) . . (+95) . . N Template:Intermediate notions short (Created page with '{{#ask: [[Stronger than::{{{1}}}]][[Weaker than::{{{2}}}]]|limit = 0|searchlabel = click here}}') (current)
- 21:12, 26 October 2009
(diff | hist) . .
**(+1,196)** . . Noetherian ring (→Relation with other properties) - 11:30, 27 March 2009 (diff | hist) . . (-21) . . Template:Top notice
- 16:52, 12 March 2009 (diff | hist) . . (-65) . . Noetherian implies every element in minimal prime is zero divisor (→Facts used) (current)
- 04:00, 9 February 2009
(diff | hist) . .
**(+2,100)** . . N Ideal generated by two prime elements in a unique factorization domain may be proper and not prime (New page: ==Statement== It is possible to have a unique factorization domain <math>R</math> and primes <math>p,q \in R</math> such that <math>(p,q)</math> is a proper ideal of <math>R</math> th...) (current) - 03:50, 9 February 2009 (diff | hist) . . (+10) . . Ideal generated by prime elements (current)
- 03:50, 9 February 2009
(diff | hist) . .
**(+594)** . . N Ideal generated by prime elements (New page: ==Statement== An '''ideal generated by prime elements''' is an ideal in an integral domain with a generating set, all of whose elements are primes. ==Relation with other properti...) - 03:47, 9 February 2009 (diff | hist) . . (+266) . . Unique factorization implies every nonzero prime ideal contains a prime element (current)
- 03:45, 9 February 2009 (diff | hist) . . (+204) . . Unique factorization and Noetherian implies every prime ideal is generated by finitely many prime elements (current)
- 03:43, 9 February 2009 (diff | hist) . . (+224) . . Unique factorization domain (→Metaproperties) (current)
- 03:34, 9 February 2009 (diff | hist) . . (+120) . . Prime ideal need not contain any prime element (→Related facts) (current)
- 03:33, 9 February 2009 (diff | hist) . . (+364) . . Prime ideal need not contain any prime element (→Related facts)
- 03:30, 9 February 2009
(diff | hist) . .
**(+2,570)** . . N Noetherian domain implies every prime ideal is generated by finitely many irreducible elements (New page: ==Statement== In a fact about::Noetherian domain (i.e., a fact about::Noetherian ring that is also an fact about::integral domain) every fact about::prime ideal is generat...) (current) - 03:29, 9 February 2009 (diff | hist) . . (+28) . . Unique factorization and Noetherian implies every prime ideal is generated by finitely many prime elements
- 03:23, 9 February 2009 (diff | hist) . . (+12) . . Permutation of regular sequence is not necessarily regular (current)
- 03:20, 9 February 2009 (diff | hist) . . (0) . . Unique factorization and Noetherian implies every prime ideal is generated by finitely many prime elements
- 03:20, 9 February 2009 (diff | hist) . . (+310) . . Unique factorization and Noetherian implies every prime ideal is generated by finitely many prime elements
- 03:19, 9 February 2009
(diff | hist) . .
**(+2,320)** . . N Unique factorization and Noetherian implies every prime ideal is generated by finitely many prime elements (New page: ==Statement== Suppose <math>R</math> is a fact about::unique factorization domain that is also a fact about::Noetherian ring; in particular, <math>R</math> is a [[fact about::Noet...) - 23:43, 8 February 2009
(diff | hist) . .
**(+1,898)** . . N Principal ideal ring implies one-dimensional (New page: {{curing property implication| stronger = principal ideal ring| weaker = one-dimensional ring}} ==Statement== ===Verbal statement=== Any principal ideal ring is a [[one-dimensional ...) (current) - 23:33, 8 February 2009
(diff | hist) . .
**(+1,889)** . . N PID implies one-dimensional (New page: {{integral domain property implication| stronger = principal ideal domain| weaker = one-dimensional domain}} ==Statement== A principal ideal domain is a one-dimensional domain. I...) (current) - 23:25, 8 February 2009 (diff | hist) . . (+106) . . Principal ideal domain (→Weaker properties)
- 23:24, 8 February 2009 (diff | hist) . . (+2) . . Principal ideal ring (→Relation with other properties) (current)
- 23:24, 8 February 2009 (diff | hist) . . (+102) . . Principal ideal ring (→Relation with other properties)
- 02:42, 7 February 2009
(diff | hist) . .
**(+1,055)** . . N Proper integrally closed subring has infinite index (New page: ==Statement== Suppose <math>S</math> is a commutative unital ring and <math>R</math> is a ''proper'' fact about::integrally closed subring of <math>S</math>. Then, <math>R</math> ...) (current) - 02:35, 7 February 2009 (diff | hist) . . (+294) . . N Linearly closed subring (New page: {{wikilocal}} {{curing-subring property}} ==Definition== A unital subring <math>S</math> of a commutative unital ring <math>R</math> is termed '''linearly closed''' if for any <m...) (current)
- 02:31, 7 February 2009 (diff | hist) . . (+187) . . Normal ring (→Metaproperties) (current)
- 02:30, 7 February 2009
(diff | hist) . .
**(+1,289)** . . N Polynomial ring over integrally closed subring is integrally closed in polynomial ring (New page: ==Statement== Suppose <math>R</math> is an fact about::integrally closed subring of a commutative unital ring <math>S</math>. Then, the polynomial ring <math>R[x]</math> is an int...) (current) - 02:17, 7 February 2009
(diff | hist) . .
**(+661)** . . N Normality is polynomial-closed (New page: {{curing metaproperty satisfaction| property = normal ring| metaproperty = polynomial-closed property of commutative unital rings}} {{integral domain metaproperty satisfaction| property = ...) (current) - 02:15, 7 February 2009 (diff | hist) . . (-8) . . Normal domain (→Metaproperties)
- 02:02, 7 February 2009
(diff | hist) . .
**(-583)** . . Unique factorization and one-dimensional iff principal ideal (current) - 02:01, 7 February 2009 (diff | hist) . . (+102) . . Unique factorization implies every nonzero prime ideal contains a prime element (→Related facts)
- 02:00, 7 February 2009
(diff | hist) . .
**(+831)** . . N Prime ideal need not contain any prime element (New page: ==Statement== It is possible to have an integral domain <math>R</math> and a nonzero fact about::prime ideal <math>P</math> of <math>R</math> such that <math>P</math> does not con...) - 01:41, 7 February 2009
(diff | hist) . .
**(+1,388)** . . N Unique factorization implies every nonzero prime ideal contains a prime element (New page: ==Statement== Suppose <math>R</math> is a fact about::unique factorization domain and <math>P</math> is a nonzero fact about::prime ideal in <math>R</math>. Then, there exists a [...) - 01:33, 7 February 2009
(diff | hist) . .
**(+1,060)** . . Noetherian ring - 00:59, 7 February 2009
(diff | hist) . .
**(+639)** . . N Unique factorization and Dedekind iff principal ideal (New page: {{definition equivalence|principal ideal domain}} ==Statement== The following are equivalent for an integral domain: * It is a fact about::unique factorization domain as well as...) (current) - 00:56, 7 February 2009
(diff | hist) . .
**(+2,078)** . . N Unique factorization and one-dimensional iff principal ideal (New page: {{definition equivalence|principal ideal domain}} ==Statement== The following are equivalent for an integral domain: * It is a unique factorization domain as well as a [[one-dim...) - 00:45, 7 February 2009 (diff | hist) . . (+118) . . Principal ideal domain (→Relation with other properties)
- 00:42, 7 February 2009 (diff | hist) . . (+396) . . N Template:Definition equivalence (New page: {{quotation|''This article gives a proof/explanation of the equivalence of multiple definitions for the term [[fact about::{{{1}}}]]'' <br> [[:Category:Proofs of equivalence of definitions...) (current)
- 00:41, 7 February 2009
(diff | hist) . .
**(+1,255)** . . N Principal ideal ring iff every prime ideal is principal (New page: {{definition equivalence|principal ideal ring}} {{definition equivalence|principal ideal domain}} ==Statement== The following are equivalent for a commutative unital ring: * Every [...) (current) - 00:25, 7 February 2009 (diff | hist) . . (+15) . . Principal ideal domain
- 00:25, 7 February 2009 (diff | hist) . . (+1) . . Template:Integral domain property (current)
- 00:24, 7 February 2009
(diff | hist) . .
**(+549)** . . Principal ideal domain - 00:23, 7 February 2009 (diff | hist) . . (+6) . . Template:Integral domain property
- 00:21, 7 February 2009 (diff | hist) . . (+2) . . Template:Integral domain property
- 00:21, 7 February 2009 (diff | hist) . . (+103) . . Template:Integral domain property
- 19:56, 6 February 2009 (diff | hist) . . (+449) . . N Template:Curing-subring property (New page: {{quotation|''This article defines a property that can be evaluated for a unital subring in a commutative unital ring: given any commutative unital ring and a subring thereof, the ...) (current)
- 19:53, 6 February 2009
(diff | hist) . .
**(+1,289)** . . Template:Integral domain property - 19:51, 6 February 2009
(diff | hist) . .
**(+1,167)** . . Template:Curing property - 19:47, 6 February 2009 (diff | hist) . . (+89) . . Template:Integral domain property non-implication (current)
- 19:47, 6 February 2009 (diff | hist) . . (+90) . . Template:Integral domain metaproperty satisfaction (current)
- 19:46, 6 February 2009 (diff | hist) . . (+336) . . N Template:Integral domain metaproperty dissatisfaction (New page: {{#if:{{{property|}}}| {{metaproperty dissatisfaction (generic)| context space = integral domain| property = {{{property}}} | metaproperty = {{{metaproperty}}} }} | {{metaproperty dissatis...) (current)
- 19:45, 6 February 2009 (diff | hist) . . (+237) . . N Template:Integral domain metaproperty satisfaction (New page: {{#if:{{{property|}}}| {{metaproperty satisfaction (generic)| context space = integral domain| property = {{{property}}} | metaproperty = {{{metaproperty}}} }} | {{metaproperty satisfactio...)
- 19:44, 6 February 2009 (diff | hist) . . (+222) . . N Template:Integral domain property non-implication (New page: {{#if:{{{stronger|}}}| {{property non-implication (generic)| context space = integral domain| stronger = {{{stronger}}} | weaker = {{{weaker}}} }} |{{property non-implication (generic)| co...)
- 19:40, 6 February 2009 (diff | hist) . . (+299) . . N Template:Integral domain property implication (New page: {{#if:{{{stronger|}}}| {{property implication (generic)| context space = integral domain| stronger = {{{stronger}}} | weaker = {{{weaker}}} }} |{{property implication (generic)| context sp...) (current)
- 19:39, 6 February 2009 (diff | hist) . . (+259) . . N Template:Curing metaproperty dissatisfaction (New page: {{#if:{{{property|}}}| {{metaproperty dissatisfaction (generic)| context space = commutative unital ring| property = {{{property}}} | metaproperty = {{{metaproperty}}} }} | {{metaproperty ...) (current)
- 19:37, 6 February 2009 (diff | hist) . . (+36) . . Template:Curing metaproperty satisfaction (current)
- 19:37, 6 February 2009 (diff | hist) . . (-254) . . Template:Curing metaproperty satisfaction
- 19:25, 6 February 2009 (diff | hist) . . (-48) . . Template:Curing property non-implication (current)
- 19:23, 6 February 2009
(diff | hist) . .
**(+1,989)** . . N Template:Metaproperty dissatisfaction (generic) (New page: {{quotation|''This article gives the statement, and possibly proof, of a [[{{{context space}}} property]] {{#if:{{{property|}}}|(i.e., [[Fact about::{{{property}}}]])}} '''not''' satisfyin...) (current) - 19:22, 6 February 2009
(diff | hist) . .
**(+1,205)** . . N Template:Metaproperty satisfaction (generic) (New page: {{quotation|''This article gives the statement, and possibly proof, of a [[{{{context space}}} property]] {{#if:{{{property|}}}|(i.e., [[Fact about::{{{property}}}]])}} satisfying a [[{{{c...) (current) - 19:12, 6 February 2009
(diff | hist) . .
**(+1,360)** . . N Template:Property non-implication (generic) (New page: {{quotation|''This article gives the statement and possibly, proof, of a non-implication relation between two [[{{{context space}}} property|{{{context space}}} properties]]. That is, it s...) (current) - 19:10, 6 February 2009 (diff | hist) . . (-445) . . Template:Curing property implication (current)
- 19:08, 6 February 2009
(diff | hist) . .
**(+1,318)** . . N Template:Property implication (generic) (New page: {{quotation|''This article gives the statement and possibly, proof, of an implication relation between two [[{{{context space}}} property|{{{context space}}} properties]]. That is, it stat...) (current) - 19:05, 6 February 2009 (diff | hist) . . (+406) . . N Characteristic subring (New page: {{curing-subring property}} ==Definition== A unital subring of a commutative unital ring is termed a '''characteristic subring''' or '''automorphism-invariant subring''' if every...) (current)
- 19:02, 6 February 2009
(diff | hist) . .
**(+547)** . . Radically closed subring (current) - 19:00, 6 February 2009 (diff | hist) . . (+1) . . Radically closed subring
- 18:59, 6 February 2009 (diff | hist) . . (+473) . . N Radically closed subring (New page: {{wikilocal}} {curing-subring property}} ==Definition== A unital subring <math>S</math> of a commutative unital ring <math>R</math> is termed '''radically closed''' if for every ...)
- 02:31, 6 February 2009
(diff | hist) . .
**(+2,116)** . . N Lagrange interpolation formula (New page: ==Statement== Suppose <math>k</math> is a field with at least <math>n + 1</math> elements. Suppose <math>x_0, x_1, \dots, x_n</math> are ''distinct'' elements of <math>k</math>. Suppo...) (current) - 02:16, 6 February 2009
(diff | hist) . .
**(+1,280)** . . N Interpolation domain (New page: {{integral domain property}} ==Definition== An integral domain <math>R</math> is termed an '''interpolation domain''' if, for any nonnegative integer <math>n</math>, there exist elem...) (current) - 02:11, 6 February 2009
(diff | hist) . .
**(+869)** . . N Ring of rational integers is an interpolation domain (New page: {{curing property satisfaction| curing = ring of rational integers| property = interpolation domain}} ==Statement== The ring of rational integers <math>\mathbb{Z}</math> is an [[inte...) (current) - 02:03, 6 February 2009
(diff | hist) . .
**(+1,662)** . . N Ring of trigonometric polynomials (New page: {{variation of|polynomial ring}} ==Definition== Let <math>R</math> be a commutative unital ring. The '''ring of trigonometric polynomials''' or '''ring of circular polynomials''' ove...) (current) - 01:52, 6 February 2009 (diff | hist) . . (+323) . . N Ring of functions from a ring to itself (New page: ==Definition== Let <math>R</math> be a commutative unital ring. The '''ring of functions''' from <math>R</math> to itself is the ring of all functions <math>f: R \to R</math> with poi...) (current)
- 01:50, 6 February 2009
(diff | hist) . .
**(+530)** . . Ring of continuous real-valued functions on a topological space (current) - 00:44, 6 February 2009 (diff | hist) . . (-73) . . Principal ideal ring (→Metaproperties)
- 00:44, 6 February 2009 (diff | hist) . . (-152) . . Principal ideal domain (→External links)
- 00:43, 6 February 2009
(diff | hist) . .
**(+623)** . . Principal ideal domain - 00:37, 6 February 2009 (diff | hist) . . (+92) . . Template:Prime-quotient-closed idp (current)
- 00:37, 6 February 2009 (diff | hist) . . (+22) . . Template:Prime-quotient-closed idp
- 00:36, 6 February 2009
(diff | hist) . .
**(+516)** . . N Template:Prime-quotient-closed idp (New page: ===Closure under quotients by prime ideals=== {{quotation|''This property of integral domains is prime-quotient-closed: the quot...) - 00:34, 6 February 2009 (diff | hist) . . (+267) . . Unique factorization domain
- 00:31, 6 February 2009 (diff | hist) . . (+456) . . Template:Localization-closed idp (current)
- 00:28, 6 February 2009 (diff | hist) . . (+138) . . Template:Localization-closed curing property (current)
- 00:25, 6 February 2009 (diff | hist) . . (-67) . . Ring of integer-valued polynomials is contained in ring generated by binomial polynomials (current)
- 00:24, 6 February 2009
(diff | hist) . .
**(+524)** . . Ring of integer-valued polynomials is contained in ring generated by binomial polynomials - 00:20, 6 February 2009
(diff | hist) . .
**(+750)** . . Ring of continuous real-valued functions on a topological space - 00:12, 6 February 2009 (diff | hist) . . (-43) . . Ring of continuous real-valued functions on a topological space
- 00:11, 6 February 2009
(diff | hist) . .
**(+892)** . . Compact space (current) - 00:07, 6 February 2009 (diff | hist) . . (+496) . . N Urysohn space (New page: ==Definition== A topological space <math>X</math> is termed a '''Urysohn space''' if given any two distinct points <math>x,y \in X</math>, there exists a continuous function <math>f:X \to...) (current)
- 00:04, 6 February 2009
(diff | hist) . .
**(+2,528)** . . N Natural map from topological space to max-spectrum of ring of continuous real-valued functions is an injection iff the space is Urysohn (New page: ==Statement== Suppose <math>X</math> is a topological space. Let <math>C(X,\R)</math> be the [[fact about::ring of continuous real-valued functions on a topological space|ring of cont...) (current) - 17:02, 5 February 2009 (diff | hist) . . (+33) . . Ring generated by binomial polynomials
- 17:01, 5 February 2009 (diff | hist) . . (+33) . . Ring of integer-valued polynomials (current)
- 17:01, 5 February 2009 (diff | hist) . . (+349) . . N Template:Variation of (New page: {{quotation|''This is a variation of [[{{{1}}}]]''<br>[[:Category:Variations of {{{1}}}|View a complete list of variations of {{{1}}}]] OR [[Varying {{{1}}}|read a survey article on varyin...) (current)
- 17:00, 5 February 2009 (diff | hist) . . (+33) . . Multivariate polynomial ring (current)
- 16:59, 5 February 2009 (diff | hist) . . (+154) . . Polynomial ring
- 16:59, 5 February 2009 (diff | hist) . . (-39) . . Polynomial ring
- 16:58, 5 February 2009 (diff | hist) . . (+39) . . Polynomial ring
- 16:57, 5 February 2009
(diff | hist) . .
**(+2,413)** . . N Euclideanness is localization-closed (New page: {{curing metaproperty satisfaction| property = Euclidean ring| metaproperty = localization-closed property of commutative unital rings}} ==Statement== Suppose <math>R</math> is a Euclide...) (current) - 16:39, 5 February 2009
(diff | hist) . .
**(+2,128)** . . N Euclideanness is quotient-closed (New page: {{curing metaproperty satisfaction| property = Euclidean ring| metaproperty = quotient-closed property of commutative unital rings}} ==Statement== Suppose <math>R</math> is a [[commutati...) (current) - 16:19, 5 February 2009
(diff | hist) . .
**(+2,475)** . . N Minimum over principal ideal of Euclidean norm is a smaller multiplicatively monotone Euclidean norm (New page: ==Statement== Suppose <math>R</math> is a commutative unital ring and <math>N</math> is a fact about::Euclidean norm on <math>R</math> -- in particular, <math>R</math> is a [[fact...) (current) - 16:09, 5 February 2009 (diff | hist) . . (+285) . . Every Euclidean ring has a unique smallest Euclidean norm (current)
- 16:08, 5 February 2009 (diff | hist) . . (+489) . . Every Euclidean ring has a unique smallest Euclidean norm
- 16:05, 5 February 2009 (diff | hist) . . (+306) . . Element of minimum norm among non-units in Euclidean ring is a universal side divisor (current)
- 16:03, 5 February 2009 (diff | hist) . . (-2) . . Element of minimum norm in Euclidean ring is a unit (g) (current)
- 16:02, 5 February 2009 (diff | hist) . . (+247) . . Element of minimum norm in Euclidean ring is a unit
- 16:01, 5 February 2009 (diff | hist) . . (-1) . . Universal side divisor implies irreducible (current)
- 16:00, 5 February 2009 (diff | hist) . . (-1) . . Element of minimum Dedekind-Hasse norm is a unit (current)
- 15:59, 5 February 2009 (diff | hist) . . (-1) . . Euclidean ring that is not a field has a universal side divisor (→Facts used) (current)
- 15:59, 5 February 2009 (diff | hist) . . (-1) . . Universal side divisor (current)
- 15:58, 5 February 2009 (diff | hist) . . (0) . . m Element of minimum norm among non-units in Euclidean ring is a universal side divisor (Element of smallest norm among non-units in Euclidean ring is a universal side divisor moved to Element of minimum norm among non-units in Euclidean ring is a universal side divisor)
- 15:58, 5 February 2009 (diff | hist) . . (+99) . . N Element of smallest norm among non-units in Euclidean ring is a universal side divisor (Element of smallest norm among non-units in Euclidean ring is a universal side divisor moved to Element of minimum norm among non-units in Euclidean ring is a universal side divisor) (current)
- 15:57, 5 February 2009
(diff | hist) . .
**(+4,742)** . . N Every Euclidean ring has a unique smallest Euclidean norm (New page: ==Statement== Every fact about::Euclidean ring (and in particular, every fact about::Euclidean domain) has a ''unique'' smallest Euclidean norm <math>N</math>. More specifically, ...) - 00:49, 5 February 2009
(diff | hist) . .
**(+3,127)** . . N Ring of integer-valued polynomials is contained in ring generated by binomial polynomials (New page: ==Statement== Suppose <math>R</math> is an integral domain of characteristic zero. Then, the [[fact about::ring of integer-valued polynomials]...) - 18:06, 4 February 2009 (diff | hist) . . (+222) . . Ring over which every nonzero polynomial has finitely many roots (→Relation with other properties) (current)
- 18:03, 4 February 2009 (diff | hist) . . (-2) . . Ring of continuous real-valued functions on a topological space (→Facts)
- 18:03, 4 February 2009 (diff | hist) . . (+262) . . Ring of continuous real-valued functions on a topological space (→Facts)
- 18:01, 4 February 2009
(diff | hist) . .
**(+1,553)** . . N Topological space maps naturally to max-spectrum of ring of continuous real-valued functions (New page: ==Statement== Suppose <math>X</math> is a topological space. Let <math>C(X,\R)</math> denote the [[fact about::ring of continuous real-valued functions on a topological space|ring of ...) (current) - 17:50, 4 February 2009
(diff | hist) . .
**(+791)** . . N Ring over which every nonzero polynomial has finitely many roots (New page: {{curing property}} ==Definition== Let <math>R</math> be a commutative unital ring. We say that <math>R</math> is a '''ring over which every nonzero polynomial has finitely many root...) - 17:43, 4 February 2009
(diff | hist) . .
**(+660)** . . N Ring over which every monic polynomial has finitely many roots (New page: {{curing property}} ==Definition== Let <math>R</math> be a commutative unital ring. We say that <math>R</math> is a '''ring over which every monic polynomial has finitely many roots'...) (current) - 17:38, 4 February 2009
(diff | hist) . .
**(+680)** . . N Ideal generated by an irreducible element (New page: {{curing-ideal property}} ==Definition== A proper nonzero ideal in a commutative unital ring is termed an '''ideal generated by an irreducible element if it satisfies the followi...) (current) - 16:22, 4 February 2009
(diff | hist) . .
**(+1,115)** . . N Irreducible element property is not determined by quotient ring (New page: ==Statement== ===In terms of elements=== The property of whether a nonzero element <math>x</math> of an integral domain (or more generally, a commutative unital ring) </math>R</m...) (current) - 16:18, 4 February 2009
(diff | hist) . .
**(+573)** . . Prime element (current) - 16:14, 4 February 2009
(diff | hist) . .
**(+526)** . . N Ring over which nonzero polynomials define nonzero functions (New page: {{curing property}} ==Definition== Suppose <math>R</math> is a commutative unital ring. We say that <math>R</math> is a '''ring over which nonzero polynomials define nonzero function...) (current) - 16:11, 4 February 2009 (diff | hist) . . (+150) . . Normal domain
- 20:20, 2 February 2009
(diff | hist) . .
**(+3,465)** . . Ring of integer-valued polynomials over rational integers is not Noetherian (current) - 19:57, 2 February 2009 (diff | hist) . . (-60) . . Gauss's lemma (current)
- 17:13, 1 February 2009 (diff | hist) . . (+113) . . Gauss's lemma
- 16:46, 1 February 2009
(diff | hist) . .
**(+507)** . . N Gauss's lemma (New page: ==Statement== Gauss's lemma states that, in a gcd domain, we have the following: * A product of primitive polynomials is primitive. * The content of a...) - 16:43, 1 February 2009
(diff | hist) . .
**(+1,120)** . . N Content of a polynomial (New page: ==Definition== Let <math>R</math> be a commutative unital ring and <math>f \in R[x]</math> be a polynomial. The content of <math>f</math> is defined as the ideal of <math>R</math>...) (current) - 16:38, 1 February 2009
(diff | hist) . .
**(+605)** . . Unique factorization domain (→Metaproperties) - 16:34, 1 February 2009 (diff | hist) . . (-7) . . Normal domain (→Ring of integer-valued polynomials)
- 16:34, 1 February 2009 (diff | hist) . . (+224) . . Normal domain (→Metaproperties)
- 16:33, 1 February 2009 (diff | hist) . . (+12) . . PID implies UFD (→Facts used) (current)
- 16:32, 1 February 2009
(diff | hist) . .
**(+751)** . . N PID implies UFD (New page: {{integral domain property implication| stronger = principal ideal domain| weaker = unique factorization domain}} ==Statement== Any principal ideal domain is a [[unique factorization...) - 16:27, 1 February 2009 (diff | hist) . . (+166) . . Ring of integer-valued polynomials over rational integers is not Noetherian
- 16:25, 1 February 2009
(diff | hist) . .
**(+2,320)** . . N Ring of integer-valued polynomials over normal domain is normal (New page: ==Statement== Suppose <math>R</math> is a fact about::normal domain. Let <math>\operatorname{Int}(R)</math> denote the fact about::ring of integer-valued polynomials over <math>R<...) (current) - 16:13, 1 February 2009
(diff | hist) . .
**(+627)** . . Ring of integer-valued polynomials - 16:08, 1 February 2009 (diff | hist) . . (+120) . . Irreducible element not implies prime (→Proof) (current)
- 16:07, 1 February 2009 (diff | hist) . . (+4) . . Irreducible element not implies prime (→Example of a ring of integer-valued polynomials)
- 16:07, 1 February 2009 (diff | hist) . . (+6) . . Irreducible element not implies prime (→Example of a ring of integer-valued polynomials)
- 16:05, 1 February 2009
(diff | hist) . .
**(+1,932)** . . N Irreducible element not implies prime (New page: ==Statement== An fact about::irreducible element in an integral domain need not be a fact about::prime element. ==Related facts== An [[integral domain in which every irreduc...) - 15:54, 1 February 2009
(diff | hist) . .
**(+1,610)** . . N Every binomial polynomial is irreducible but not prime in the ring of integer-valued polynomials over rational integers (New page: ==Statement== In the ring of integer-valued polynomials over rational integers, every binomial polynomial, i.e., every polynomial of the form: <math>\binom{x}{r}</math> is an [[fact...) (current) - 15:46, 1 February 2009
(diff | hist) . .
**(+819)** . . N Ring of integer-valued polynomials over rational integers is not a UFD (New page: {{integral domain property dissatisfaction| domain = ring of integer-valued polynomials over rational integers| property = unique factorization domain}} ==Statement== The [[ring of integ...) (current) - 15:42, 1 February 2009
(diff | hist) . .
**(+861)** . . N Ring of integer-valued polynomials over rational integers is not Noetherian (New page: {{integral domain property dissatisfaction| domain = ring of integer-valued polynomials over rational integers| propertyringform = Noetherian ring| propertydomainform = Noetherian domain}}...) - 15:36, 1 February 2009
(diff | hist) . .
**(+2,059)** . . N Ring of continuous real-valued functions on a topological space (New page: ==Definition== The '''ring of continuous real-valued functions on a topological space''' is defined as the ring of all continuous functions from the topologi...) - 23:54, 31 January 2009
(diff | hist) . .
**(+867)** . . N Every irreducible is prime implies any two irreducible factorizations are equal upto ordering and associates (New page: {{integral domain property implication| stronger = integral domain in which every irreducible is prime| weaker = integral domain in which any two irreducible factorizations are equal upto ...) (current) - 23:51, 31 January 2009
(diff | hist) . .
**(+708)** . . N Prime factorization of element is unique irreducible factorization upto ordering and associates (New page: ==Statement== Suppose <math>R</math> is an integral domain, and <math>a \in R</math> is a nonzero non-unit with a factorization into primes: <math>a = up_1p_2 \dots p_r</math> where...) (current) - 23:36, 31 January 2009
(diff | hist) . .
**(+767)** . . N Integral domain in which any two irreducible factorizations are equal upto ordering and associates (New page: {{integral domain property}} ==Definition== An '''integral domain in which any two irreducible factorizations are equal upto ordering and associates''' is an integral domain satisfyi...) - 23:28, 31 January 2009
(diff | hist) . .
**(+664)** . . N Integral domain in which every irreducible is prime (New page: {{integral domain property}} ==Definition== An '''integral domain in which every irreducible is prime''' is an integral domain satisfying the following equivalent condition: every [[...) (current) - 23:10, 31 January 2009
(diff | hist) . .
**(+1,062)** . . N Unique factorization and Bezout iff principal ideal (New page: ==Statement== The following are equivalent for an integral domain: * It is a fact about::principal ideal domain. * It is both a fact about::unique factorization domain and a ...) (current) - 23:00, 31 January 2009 (diff | hist) . . (-7) . . Principal ideal domain admits multiplicative Dedekind-Hasse norm (→Facts used) (current)
- 23:00, 31 January 2009
(diff | hist) . .
**(+1,075)** . . Principal ideal domain admits multiplicative Dedekind-Hasse norm - 22:50, 31 January 2009
(diff | hist) . .
**(+930)** . . N Length of irreducible factorization is strictly multiplicatively monotone on unique factorization domain (New page: ==Statement== Suppose <math>R</math> is a fact about::unique factorization domain. Define <math>N: R \setminus \{ 0 \} \to \mathbb{N}_0</math> as follows: * <math>N(u) = 0</math> for...) (current) - 22:42, 31 January 2009
(diff | hist) . .
**(+1,704)** . . N Strictly multiplicatively monotone norm on Bezout domain is a Dedekind-Hasse norm (New page: ==Statement== Suppose <math>R</math> is a fact about::Bezout domain (i.e., it is an integral domain that is also a fact about::Bezout ring: every finitely generated ideal on <...) (current) - 22:31, 31 January 2009 (diff | hist) . . (-31) . . Universal side divisor implies irreducible
- 22:29, 31 January 2009 (diff | hist) . . (+124) . . Prime element
- 22:28, 31 January 2009
(diff | hist) . .
**(+629)** . . Irreducible element (current) - 22:18, 31 January 2009 (diff | hist) . . (+129) . . Principal ideal domain (→Conjunction expressions)
- 22:17, 31 January 2009
(diff | hist) . .
**(+555)** . . N Strictly multiplicatively monotone norm (New page: {{wikilocal}} {{curing-norm property}} ==Definition== A '''strictly multiplicatively monotone norm''' on a commutative unital ring <math>R</math> is a function <math>N: R \setminus \{ 0 ...) (current) - 22:11, 31 January 2009 (diff | hist) . . (+101) . . Multiplicatively monotone norm (current)
- 22:06, 31 January 2009 (diff | hist) . . (+125) . . Geometric condition for imaginary quadratic integer ring to be norm-Euclidean (current)
- 22:05, 31 January 2009
(diff | hist) . .
**(+575)** . . N Geometric condition for imaginary quadratic integer ring to be norm-Euclidean (New page: ==Statement== Suppose <math>\mathcal{O}</math> is an imaginary quadratic integer ring. Then, <math>\mathcal{O}</math> is a fact about::norm-Euclidean ring of integers if and only ...) - 21:59, 31 January 2009 (diff | hist) . . (+196) . . Euclidean ring that is not a field has a universal side divisor
- 21:58, 31 January 2009 (diff | hist) . . (0) . . Universal side divisor
- 21:58, 31 January 2009 (diff | hist) . . (+118) . . Element of minimum norm among non-units in Euclidean ring is a universal side divisor
- 21:57, 31 January 2009
(diff | hist) . .
**(+2,044)** . . Universal side divisor - 20:30, 31 January 2009
(diff | hist) . .
**(+2,526)** . . N Irreducible not implies universal side divisor (New page: ==Statement== An fact about::irreducible element in an integral domain need not be a fact about::universal side divisor. In fact, an irreducible element need not be a universa...) (current) - 20:18, 31 January 2009
(diff | hist) . .
**(+1,676)** . . Ring of rational integers is not uniquely Euclidean for any norm (current) - 19:01, 31 January 2009 (diff | hist) . . (+225) . . N Ring of rational integers is not uniquely Euclidean for any norm (New page: {{curing property dissatisfaction| curing = ring of rational integers| property = uniquely Euclidean domain}} ==Statement== The ring of rational integers cannot be made a [[uniquely ...)
- 18:55, 31 January 2009
(diff | hist) . .
**(+922)** . . N Ring of rational integers is Euclidean with norm equal to binary logarithm of absolute value (New page: {{curing property satisfaction| curing = ring of rational integers| property = Euclidean domain}} ==Statement== The ring of rational integers <math>\mathbb{Z}</math> is a [[Euclidean...) (current) - 18:46, 31 January 2009 (diff | hist) . . (+190) . . Ring of rational integers is Euclidean with norm equal to absolute value (current)
- 18:44, 31 January 2009
(diff | hist) . .
**(+3,228)** . . N Integral domain satisfying ACCP that is not a field has either infinitely many units or infinitely many associate classes of irreducibles (New page: ==Statement== Suppose <math>R</math> is an fact about::integral domain that is also a fact about::ring satisfying ACCP: it satisfies the ascending chain condition on [[principal i...) (current) - 18:28, 31 January 2009
(diff | hist) . .
**(+3,160)** . . N Unique factorization domain that is not a field has either infinitely many units or infinitely many associate classes of irreducibles (New page: ==Statement== Suppose <math>R</math> is a fact about::unique factorization domain that is not a field. Then, at least one of these is true for <math>R</math>: * <math>R</math> ha...) (current) - 17:54, 31 January 2009
(diff | hist) . .
**(+2,020)** . . N Universal side divisor implies irreducible (New page: ==Statement== In an integral domain, any fact about::universal side divisor is an fact about::irreducible element. ==Related facts== ===Converse=== The converse is not true...) - 17:46, 31 January 2009 (diff | hist) . . (+332) . . Irreducible element
- 20:26, 26 January 2009
(diff | hist) . .
**(+525)** . . Norm-Euclidean ring of integers (current) - 20:22, 26 January 2009
(diff | hist) . .
**(+572)** . . N Classification of norm-Euclidean imaginary quadratic integer rings (New page: ==Statement== The following are the precise values of <math>D < 0</math>, <math>D</math> square-free for which the imaginary quadratic integer ring corresponding to <math>D</math> is a [[...) (current) - 03:04, 24 January 2009
(diff | hist) . .
**(+993)** . . N Ring of integer-valued polynomials over rational integers (New page: ==Definition== ===Symbol-free definition=== The '''ring of integer-valued polynomials over rational integers''' is defined in the following equivalent ways: * It is the [[ring of intege...) (current) - 02:59, 24 January 2009 (diff | hist) . . (+218) . . Ring generated by binomial polynomials
- 02:57, 24 January 2009
(diff | hist) . .
**(+982)** . . N Ring generated by binomial polynomials (New page: ==Definition== Let <math>R</math> be a commutative unital ring of characteristic zero. Let <math>K</math> be the quotient ring of <math>R</math> by th...) - 02:49, 24 January 2009
(diff | hist) . .
**(+1,470)** . . N Ring of integer-valued polynomials (New page: ==Definition== Let <math>R</math> be an integral domain and let <math>K</math> be its field of fractions. The '''ring of integer-valued polynomials''' for <math>R</math>, denoted ...) - 02:33, 24 January 2009 (diff | hist) . . (+91) . . Imaginary quadratic number field (→Facts) (current)
- 02:33, 24 January 2009 (diff | hist) . . (0) . . Imaginary quadratic number field (→Norm-Euclidean imaginary quadratic number fields)
- 02:32, 24 January 2009 (diff | hist) . . (0) . . m Ring of rational integers is Euclidean with norm equal to absolute value (Ring of integers is Euclidean with norm equal to absolute value moved to Ring of rational integers is Euclidean with norm equal to absolute value)
- 02:32, 24 January 2009 (diff | hist) . . (+86) . . N Ring of integers is Euclidean with norm equal to absolute value (Ring of integers is Euclidean with norm equal to absolute value moved to Ring of rational integers is Euclidean with norm equal to absolute value) (current)
- 02:31, 24 January 2009
(diff | hist) . .
**(+1,581)** . . Imaginary quadratic number field - 02:28, 24 January 2009 (diff | hist) . . (+28) . . Norm-Euclidean ring of integers
- 02:26, 24 January 2009 (diff | hist) . . (+66) . . Norm on a commutative unital ring (current)
- 02:06, 24 January 2009
(diff | hist) . .
**(+544)** . . N Number field with positive algebraic norm (New page: {{number field property}} ==Statement== A '''number field with positive algebraic norm''' is a number field such that the algebraic norm of any n...) (current) - 02:02, 24 January 2009 (diff | hist) . . (+448) . . N Imaginary quadratic number field (New page: {{number field property}} ==Definition== An '''imaginary quadratic number field''' is a number field obtained as a quadratic extension of the field of rational numbers by the squ...)
- 01:55, 24 January 2009 (diff | hist) . . (0) . . Real quadratic number field (→Definition) (current)
- 01:55, 24 January 2009 (diff | hist) . . (+2) . . Real quadratic number field
- 01:55, 24 January 2009
(diff | hist) . .
**(+563)** . . N Real quadratic number field (New page: {{number field property}} ==Definition== A '''real quadratic number field''' is a number field obtained by extending the field of rational numbers]] by the squareroot of a positive s...) - 01:52, 24 January 2009 (diff | hist) . . (+137) . . N Category:Number field properties (New page: This category lists properties that can be evaluated for number fields: finite field extensions of the field of rational numbers.) (current)
- 01:51, 24 January 2009
(diff | hist) . .
**(+969)** . . N Algebraic norm in a number field (New page: ==Definition== The '''algebraic norm in a number field''' is a map from the number field to the field of rational numbers, defined as follows. If the number field has degree <math>d</...) (current) - 01:46, 24 January 2009 (diff | hist) . . (+154) . . Associate elements (current)
- 01:45, 24 January 2009
(diff | hist) . .
**(+1,580)** . . N Greatest common divisor (New page: ==Statement== ===For a finite sequence=== Let <math>R</math> be a commutative unital ring and <math>a_1, a_2, \dots, a_n \in R</math>. An element <math>d \in R</math> is termed a '''...) (current) - 01:37, 24 January 2009 (diff | hist) . . (+27) . . Gcd domain (current)
- 01:17, 24 January 2009 (diff | hist) . . (+468) . . N Filtrative norm (New page: {{curing-norm property}} ==Definition== A norm on a commutative unital ring is termed '''filtrative''' if it is a function from the nonzero elements of the ring to ''nonnegative'' in...) (current)
- 01:14, 24 January 2009
(diff | hist) . .
**(+1,286)** . . N Polynomial ring over a field is uniquely Euclidean with norm equal to degree (New page: {{curing property implication| stronger = polynomial ring over a field| weaker = uniquely Euclidean domain}} ==Statement== Suppose <math>k</math> is a field, and <math>k[x]</math> is...) (current) - 01:09, 24 January 2009 (diff | hist) . . (+9) . . Euclidean domain (→Examples)
- 01:04, 24 January 2009
(diff | hist) . .
**(+1,906)** . . N Associate implies same orbit under multiplication by group of units in integral domain (New page: ==Statement== Suppose <math>R</math> is a fact about::integral domain and <math>a,b \in R</math> are fact about::associate elements in <math>R</math>. Then, there exists a unit <m...) (current) - 00:56, 24 January 2009 (diff | hist) . . (+239) . . Elements in same orbit under multiplication by group of units are associate (current)
- 00:55, 24 January 2009
(diff | hist) . .
**(+1,223)** . . N Elements in same orbit under multiplication by group of units are associate (New page: ==Statement== Suppose <math>R</math> is a commutative unital ring and <math>a,b \in R</math> are elements such that there exists a unit <math>u \in R</math> such that <math>b = au</ma...) - 21:25, 23 January 2009 (diff | hist) . . (+257) . . Associate elements
- 21:21, 23 January 2009 (diff | hist) . . (+14) . . Multiplicatively monotone norm is constant on associate classes (current)
- 21:20, 23 January 2009 (diff | hist) . . (0) . . m Multiplicatively monotone norm is constant on associate classes (Multiplicatively monotone Euclidean norm is constant on associate classes moved to Multiplicatively monotone norm is constant on associate classes)
- 21:20, 23 January 2009 (diff | hist) . . (+77) . . N Multiplicatively monotone Euclidean norm is constant on associate classes (Multiplicatively monotone Euclidean norm is constant on associate classes moved to Multiplicatively monotone norm is constant on associate classes) (current)
- 21:19, 23 January 2009
(diff | hist) . .
**(+1,800)** . . N Ring of rational integers is Euclidean with norm equal to absolute value (New page: {{curing property satisfaction| curing = ring of rational integers| property = Euclidean domain}} ==Statement== ===Main statement=== Consider <math>\mathbb{Z}</math>, the [[ring of rati...) - 21:11, 23 January 2009 (diff | hist) . . (+282) . . N Automorphism-invariant norm (New page: {{curing-norm property}} ==Definition== A norm on a commutative unital ring is termed an '''automorphism-invariant norm''' if for any nonzero element of the ring and any [[automorphi...) (current)
- 21:08, 23 January 2009 (diff | hist) . . (+248) . . Automorphism-invariant Euclidean norm (current)
- 21:05, 23 January 2009 (diff | hist) . . (0) . . Template:Curing-norm property conjunction (current)
- 21:05, 23 January 2009 (diff | hist) . . (+52) . . Automorphism-invariant Euclidean norm
- 21:03, 23 January 2009 (diff | hist) . . (0) . . m Automorphism-invariant Euclidean norm (Characteristic Euclidean norm moved to Automorphism-invariant Euclidean norm)
- 21:03, 23 January 2009 (diff | hist) . . (+51) . . N Characteristic Euclidean norm (Characteristic Euclidean norm moved to Automorphism-invariant Euclidean norm) (current)
- 21:02, 23 January 2009 (diff | hist) . . (+97) . . Filtrative and multiplicatively monotone Euclidean implies uniquely Euclidean (current)
- 21:01, 23 January 2009 (diff | hist) . . (+1) . . Template:Curing-norm property conjunction
- 21:01, 23 January 2009
(diff | hist) . .
**(+720)** . . N Template:Curing-norm property conjunction (New page: {{quotation|''This article defines a property of a norm in a commutative unital ring obtained as the conjunction of two properties: [[conjunction involving::{{{1}}}]][[defining ingredi...) - 20:58, 23 January 2009
(diff | hist) . .
**(+544)** . . N Multiplicative Dedekind-Hasse norm (New page: {{curing-norm property conjunction|multiplicative norm|Dedekind-Hasse norm}} ==Definition== A '''multiplicative Dedekind-Hasse norm''' on a commutative unital ring is a function from...) (current) - 19:57, 23 January 2009 (diff | hist) . . (0) . . m Filtrative and multiplicatively monotone Euclidean implies uniquely Euclidean (Filtrative and multiplicatively monotone implies uniquely Euclidean moved to Filtrative and multiplicatively monotone Euclidean implies uniquely Euclidean)
- 19:57, 23 January 2009 (diff | hist) . . (+91) . . N Filtrative and multiplicatively monotone implies uniquely Euclidean (Filtrative and multiplicatively monotone implies uniquely Euclidean moved to Filtrative and multiplicatively monotone Euclidean implies uniquely Euclidean) (current)
- 19:57, 23 January 2009 (diff | hist) . . (+98) . . Multiplicatively monotone norm (→Facts)
- 19:56, 23 January 2009
(diff | hist) . .
**(+696)** . . N Multiplicatively monotone norm (New page: {{curing-norm property}} ==Definition== A '''multiplicatively monotone norm''' on a commutative unital ring is a function from its nonzero elements to the integers with the property ...) - 19:51, 23 January 2009 (diff | hist) . . (+164) . . N Principal ideal domain admits multiplicative Dedekind-Hasse norm (New page: ==Statement== Suppose <math>R</math> is a fact about::principal ideal domain. Then, <math>R</math> admits a fact about::multiplicative Dedekind-Hasse norm.)
- 19:50, 23 January 2009
(diff | hist) . .
**(+848)** . . N Multiplicative norm (New page: {{curing-norm property}} ==Definition== A '''multiplicative norm''' on a commutative unital ring is a function from the nonzero elements of the commutative unital ring to the integer...) (current) - 19:46, 23 January 2009 (diff | hist) . . (+262) . . Multiplicative Euclidean norm (current)
- 19:41, 23 January 2009 (diff | hist) . . (+374) . . N Template:Curing-norm property (New page: {{quotation|''This article defines a property that can be evaluated for a norm on a commutative unital ring: a function from the nonzero elements of the ring to the integers.<br>[[:Cat...) (current)
- 19:40, 23 January 2009 (diff | hist) . . (+441) . . N Nonnegative norm (New page: {{curing-norm property}} ==Definition== A norm on a commutative unital ring <math>R</math> (i.e., a function from the nonzero elements of <math>R</math> to the integers) is termed ''...) (current)
- 19:38, 23 January 2009 (diff | hist) . . (+111) . . Norm on a commutative unital ring
- 19:37, 23 January 2009
(diff | hist) . .
**(+1,210)** . . N Norm on a commutative unital ring (New page: ==Definition== Let <math>R</math> be a commutative unital ring. A '''norm''' on <math>R</math> is a function from the nonzero elements of <math>R</math> to the nonnegative integers. ...) - 19:28, 23 January 2009
(diff | hist) . .
**(+1,232)** . . N Element of minimum Dedekind-Hasse norm is a unit (New page: ==Statement== Suppose <math>R</math> is a commutative unital ring and <math>N</math> is a fact about::Dedekind-Hasse norm on <math>R</math>. Then, the set: <math>\{ b \in R \setm...) - 18:32, 23 January 2009
(diff | hist) . .
**(+1,623)** . . N Euclidean implies Dedekind-Hasse (New page: ==Statement== ===Verbal statement=== Any fact about::Euclidean norm on a commutative unital ring is a fact about::Dedekind-Hasse norm. ==Definitions used== ===Euclidean nor...) (current) - 18:25, 23 January 2009 (diff | hist) . . (0) . . m Euclidean norm (Euclidean norm on a commutative unital ring moved to Euclidean norm) (current)
- 18:25, 23 January 2009 (diff | hist) . . (+28) . . N Euclidean norm on a commutative unital ring (Euclidean norm on a commutative unital ring moved to Euclidean norm) (current)
- 18:24, 23 January 2009 (diff | hist) . . (-4) . . Dedekind-Hasse norm (→Relation with other properties) (current)
- 18:24, 23 January 2009 (diff | hist) . . (+315) . . Dedekind-Hasse norm
- 18:23, 23 January 2009
(diff | hist) . .
**(+2,169)** . . N Dedekind-Hasse norm implies principal ideal ring (New page: ==Statement== A commutative unital ring that admits a fact about::Dedekind-Hasse norm must be a fact about::principal ideal ring. In particular, an [[fact about::integral dom...) (current) - 18:10, 23 January 2009
(diff | hist) . .
**(+707)** . . N Dedekind-Hasse norm (New page: ==Statement== A '''Dedekind-Hasse norm''' on a commutative unital ring <math>R</math> is a function <math>N</math> from the nonzero elements of <math>R</math> to the set of nonnegativ...) - 18:08, 23 January 2009 (diff | hist) . . (-5) . . Principal ideal domain
- 02:30, 23 January 2009
(diff | hist) . .
**(+2,454)** . . Euclidean domain - 00:05, 23 January 2009 (diff | hist) . . (+251) . . PID not implies Euclidean (current)
- 00:00, 23 January 2009 (diff | hist) . . (+24) . . Euclidean ring that is not a field has a universal side divisor
- 23:59, 22 January 2009
(diff | hist) . .
**(+705)** . . N Euclidean ring that is not a field has a universal side divisor (New page: ==Statement== Suppose <math>R</math> is a Euclidean ring that is not a field. Then, <math>R</math> has a universal side divisor. ==Definitions used== ===Euclidean ring, Eucl...) - 23:57, 22 January 2009 (diff | hist) . . (-1) . . Universal side divisor (→Facts)
- 23:56, 22 January 2009 (diff | hist) . . (+92) . . Universal side divisor (→Facts)
- 23:55, 22 January 2009
(diff | hist) . .
**(+1,716)** . . N Element of minimum norm among non-units in Euclidean ring is a universal side divisor (New page: ==Statement== Suppose <math>R</math> is a commutative unital ring and <math>N</math> is a fact about::Euclidean norm on <math>R</math> -- in particular, <math>R</math> is a [[fact...) - 23:53, 22 January 2009 (diff | hist) . . (+48) . . Universal side divisor
- 23:35, 22 January 2009 (diff | hist) . . (+8) . . Universal side divisor
- 23:34, 22 January 2009
(diff | hist) . .
**(+1,276)** . . N Multiplicatively monotone Euclidean norm admits unique Euclidean division for exact divisor (New page: ==Statement== Suppose <math>R</math> is an commutative unital ring with a fact about::Euclidean norm <math>N</math> that is [[fact about::multiplicatively monotone Euclidean norm|...) (current) - 23:12, 22 January 2009
(diff | hist) . .
**(+1,092)** . . N Multiplicatively monotone norm is constant on associate classes (New page: ==Statement== Suppose <math>R</math> is a commutative unital ring and <math>N</math> is a fact about::Euclidean norm on <math>R</math> that is [[fact about::multiplicatively monot...) - 22:41, 22 January 2009
(diff | hist) . .
**(+543)** . . Multiplicatively monotone Euclidean norm (current) - 22:37, 22 January 2009 (diff | hist) . . (+79) . . Filtrative and multiplicatively monotone Euclidean implies uniquely Euclidean
- 22:37, 22 January 2009
(diff | hist) . .
**(+2,588)** . . N Filtrative and multiplicatively monotone Euclidean implies uniquely Euclidean (New page: ==Statement== Suppose <math>R</math> is an integral domain with a fact about::Euclidean norm <math>N</math> satisfying the following two conditions: * <math>N</math> is a [[fact ...) - 17:21, 22 January 2009 (diff | hist) . . (+289) . . Filtrative Euclidean norm (current)
- 17:17, 22 January 2009 (diff | hist) . . (+436) . . N Subadditive Euclidean norm (New page: {{Euclidean norm property}} ==Definition== Let <math>R</math> be a commutative unital ring and <math>N</math> be a Euclidean norm on <math>R</math>. We say that <math>N</math> is...) (current)
- 17:15, 22 January 2009
(diff | hist) . .
**(+957)** . . N Multiplicatively monotone Euclidean norm (New page: {{Euclidean norm property}} ==Definition== A Euclidean norm is termed '''multiplicatively monotone''' if the norm of a product of two elements is at least equal to the norms of the e...) - 17:10, 22 January 2009 (diff | hist) . . (-298) . . Filtrative Euclidean norm
- 17:04, 22 January 2009
(diff | hist) . .
**(+1,010)** . . N Element of minimum norm in Euclidean ring is a unit (New page: ==Statement== Suppose <math>R</math> is a Euclidean ring, i.e., <math>R</math> is a commutative unital ring with a Euclidean norm <math>N</math>. Suppose <math>b \in R</math> ...) - 16:53, 22 January 2009 (diff | hist) . . (+82) . . Euclidean domain (→Definition)
- 16:25, 22 January 2009 (diff | hist) . . (+431) . . N Universal side divisor (New page: ==Definition== A nonzero element <math>x</math> in an integral domain <math>R</math> is termed a '''universal side divisor''' if <math>x</math> satisfies the following two conditions:...)
- 16:37, 20 January 2009 (diff | hist) . . (+221) . . Local ring (current)
- 23:06, 19 January 2009
(diff | hist) . .
**(+1,077)** . . Noetherian not implies zero divisor in minimal prime (current) - 23:00, 19 January 2009
(diff | hist) . .
**(-737)** . . Main Page (Replacing page with '{{top notice}}') (current) - 19:11, 18 January 2009 (diff | hist) . . (+415) . . N Noetherian not implies zero divisor in minimal prime (New page: ==Statement== It is possible to have a fact about::Noetherian ring with a fact about::zero divisor that is ''not'' contained in ''any'' fact about::minimal prime ideal. ==Rel...)
- 19:08, 18 January 2009 (diff | hist) . . (+159) . . Reduced Noetherian implies zero divisor in minimal prime (→Related facts) (current)
- 19:07, 18 January 2009 (diff | hist) . . (+3) . . Noetherian ring has finitely many minimal primes and every prime contains a minimal prime (→Facts used) (current)
- 19:06, 18 January 2009 (diff | hist) . . (+1) . . Noetherian ring has finitely many minimal primes and every prime contains a minimal prime (→Facts used)
- 19:06, 18 January 2009 (diff | hist) . . (+48) . . Noetherian ring has finitely many minimal primes and every prime contains a minimal prime
- 19:05, 18 January 2009 (diff | hist) . . (+40) . . Noetherian implies every element in minimal prime is zero divisor
- 19:05, 18 January 2009 (diff | hist) . . (+12) . . Reduced Noetherian implies zero divisor in minimal prime (→Statement)
- 19:05, 18 January 2009 (diff | hist) . . (+2) . . Reduced Noetherian implies zero divisor in minimal prime (→Statement)
- 19:04, 18 January 2009
(diff | hist) . .
**(+736)** . . Reduced Noetherian implies zero divisor in minimal prime - 18:44, 18 January 2009 (diff | hist) . . (-2) . . Reduced Noetherian implies zero divisor in minimal prime (→Proof)
- 20:26, 17 January 2009 (diff | hist) . . (+54) . . Primary ideal (→Relation with other properties)
- 20:25, 17 January 2009 (diff | hist) . . (+99) . . Prime ideal
- 20:23, 17 January 2009 (diff | hist) . . (+28) . . Intersection of maximal ideals (→Relation with other properties) (current)
- 20:22, 17 January 2009 (diff | hist) . . (+45) . . Maximal ideal (→Relation with other properties) (current)
- 20:22, 17 January 2009 (diff | hist) . . (-30) . . Radical ideal (→Incomparable properties)
- 20:21, 17 January 2009 (diff | hist) . . (+56) . . Radical ideal (→Relation with other properties)
- 17:27, 17 January 2009 (diff | hist) . . (+426) . . Principal ideal domain (→Relation with other properties)
- 17:24, 17 January 2009
(diff | hist) . .
**(+509)** . . Principal ideal domain - 17:21, 17 January 2009 (diff | hist) . . (+325) . . Unique factorization domain (→Relation with other properties)
- 17:19, 17 January 2009 (diff | hist) . . (+52) . . Gcd domain (→Relation with other properties)
- 17:19, 17 January 2009 (diff | hist) . . (+173) . . Bezout domain (→Relation with other properties)
- 17:18, 17 January 2009 (diff | hist) . . (+77) . . Bezout domain (→Relation with other properties)
- 17:17, 17 January 2009 (diff | hist) . . (+310) . . Dedekind domain
- 17:15, 17 January 2009 (diff | hist) . . (+22) . . Cohen-Macaulay ring (→Relation with other properties)
- 17:14, 17 January 2009 (diff | hist) . . (+438) . . Noetherian ring (→Relation with other properties)
- 17:12, 17 January 2009 (diff | hist) . . (+349) . . Zero-dimensional ring (→Relation with other properties) (current)
- 17:10, 17 January 2009 (diff | hist) . . (+125) . . One-dimensional domain (→Relation with other properties) (current)
- 17:08, 17 January 2009 (diff | hist) . . (+405) . . Cohen-Macaulay ring (→Relation with other properties)
- 16:57, 17 January 2009
(diff | hist) . .
**(+652)** . . Noetherian ring (→Relation with other properties) - 16:53, 17 January 2009 (diff | hist) . . (+43) . . Principal ideal ring (→Relation with other properties)
- 16:53, 17 January 2009 (diff | hist) . . (+80) . . Noetherian ring (→Relation with other properties)
- 15:49, 16 January 2009 (diff | hist) . . (+287) . . MediaWiki:Sidebar (current)
- 15:40, 16 January 2009
(diff | hist) . .
**(+1,055)** . . N Commalg:General disclaimer (New page: This is a general disclaimer common to all subject wikis, with the source at Ref:Ref:General disclaimer. For specific hazards of using this particular subject wiki, refer [[{{SITENAME}...) (current) - 01:44, 16 January 2009
(diff | hist) . .
**(+2,096)** . . N Commalg:Privacy policy (New page: This privacy policy is common to subject wikis. For the original privacy policy, refer Ref:Ref:Privacy policy. ==Privacy for readers== If you are surfing this website, your actions a...) (current) - 23:15, 15 January 2009 (diff | hist) . . (+226) . . MediaWiki:Sitenotice
- 22:52, 15 January 2009 (diff | hist) . . (+11) . . MediaWiki:Sidebar
- 22:38, 15 January 2009 (diff | hist) . . (+34) . . MediaWiki:Sitenotice
- 22:37, 15 January 2009 (diff | hist) . . (-10) . . MediaWiki:Sitenotice
- 22:35, 15 January 2009 (diff | hist) . . (+13) . . N Template:Sitestatus (New page: pre-pre-alpha) (current)
- 22:19, 15 January 2009
(diff | hist) . .
**(+4,123)** . . Commalg:Copyrights (current) - 22:18, 15 January 2009 (diff | hist) . . (+37) . . N Template:Fullsitetitle (New page: Commalg, The Commutative Algebra Wiki) (current)
- 22:01, 15 January 2009 (diff | hist) . . (+1) . . Template:Top notice
- 21:58, 15 January 2009 (diff | hist) . . (+359) . . N Template:Top notice (New page: {{quotation|Welcome to '''Commalg (The Commutative Algebra Wiki)'''. This is a pre-pre-alpha stage commutative algebra wiki primarily managed by Vipul Naik, a Ph.D. student ...)
- 12:19, 3 January 2009 (diff | hist) . . (+216) . . Nm User talk:Masnevets (Welcome!) (current)
- 12:19, 3 January 2009 (diff | hist) . . (+218) . . Nm User:Masnevets (Creating user page with biography of new user.) (current)
- 17:02, 11 September 2008 (diff | hist) . . (+9) . . MediaWiki:Sidebar
- 16:59, 11 September 2008 (diff | hist) . . (+89) . . N MediaWiki:Sitenotice (New page: 75px|right The Commutative Algebra Wiki (pre-pre-alpha))
- 16:58, 11 September 2008 (diff | hist) . . (0) . . N File:Logo.jpg (current)
- 16:57, 11 September 2008 (diff | hist) . . (+54) . . MediaWiki:Sidebar
- 18:34, 5 August 2008 (diff | hist) . . (+208) . . Main Page
- 18:34, 5 August 2008 (diff | hist) . . (+153) . . Template:Quotation
- 18:32, 5 August 2008
(diff | hist) . .
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