Intersection of maximal ideals - Revision history

Vipul: /* Relation with other properties */

2009-01-17T20:23:11Z

Relation with other properties

← Older revision		Revision as of 20:23, 17 January 2009
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	===Stronger properties===		===Stronger properties===

	* [[Maximal ideal]]		* [[Weaker than::Maximal ideal]]

	===Weaker properties===		===Weaker properties===

	* [[Radical ideal]]: {{proofat\|[[Intersection of maximal ideals implies radical]]}}		* [[Stronger than::Radical ideal]]: {{proofat\|[[Intersection of maximal ideals implies radical]]}}

	===Related ring properties===		===Related ring properties===

Vipul: 5 revisions

2008-05-12T16:23:55Z

5 revisions

← Older revision	Revision as of 16:23, 12 May 2008
(No difference)

Vipul at 15:25, 24 January 2008

2008-01-24T15:25:23Z

← Older revision		Revision as of 15:25, 24 January 2008
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	An [[ideal]] in a [[commutative unital ring]] is termed an '''intersection of maximal ideals''' if it can be expressed as an intersection of [[maximal ideal]]s (this is really a tautological definition).		An [[ideal]] in a [[commutative unital ring]] is termed an '''intersection of maximal ideals''' if it can be expressed as an intersection of [[maximal ideal]]s (this is really a tautological definition).

			Note that although a maximal ideal is assumed to be proper, an ''intersection of maximal ideals'' could be the whole ring, i.e. we allow the empty intersection.
	==Relation with other properties==		==Relation with other properties==

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	A ring in which every radical ideal is an intersection of maximal ideals is termed a [[Jacobson ring]] (or sometimes a Hilbert ring).		A ring in which every radical ideal is an intersection of maximal ideals is termed a [[Jacobson ring]] (or sometimes a Hilbert ring).

			==Metaproperties==

			{{intersection-closed ideal property}}

Vipul: /* Relation with other properties */

2008-01-10T01:11:55Z

Relation with other properties

← Older revision		Revision as of 01:11, 10 January 2008
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	===Weaker properties===		===Weaker properties===

	* [[Radical ideal]]		* [[Radical ideal]]: {{proofat\|[[Intersection of maximal ideals implies radical]]}}

			===Related ring properties===

			A ring in which every radical ideal is an intersection of maximal ideals is termed a [[Jacobson ring]] (or sometimes a Hilbert ring).

Vipul at 00:08, 19 December 2007

2007-12-19T00:08:38Z

← Older revision		Revision as of 00:08, 19 December 2007
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	{{curing-ideal property}}		{{curing-ideal property}}

	{{quotient is a\|semisimple ring}		{{quotient is a\|semisimple ring}}

	==Definition==		==Definition==

Vipul at 00:08, 19 December 2007

2007-12-19T00:08:28Z

← Older revision		Revision as of 00:08, 19 December 2007
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	{{curing-ideal property}}		{{curing-ideal property}}

	{{quotient is a\|[[semisimple ring~~]]}~~}		{{quotient is a\|semisimple ring}

	==Definition==		==Definition==

Vipul at 22:17, 18 December 2007

2007-12-18T22:17:36Z

New page

{{curing-ideal property}}

{{quotient is a|[[semisimple ring]]}}

==Definition==

===Symbol-free definition===

An [[ideal]] in a [[commutative unital ring]] is termed an '''intersection of maximal ideals''' if it can be expressed as an intersection of [[maximal ideal]]s (this is really a tautological definition).

==Relation with other properties==

===Stronger properties===

* [[Maximal ideal]]

===Weaker properties===

* [[Radical ideal]]