# 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 ...)

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