Regular local ring - Revision history

Vipul: 6 revisions

2008-05-12T16:34:05Z

6 revisions

← Older revision	Revision as of 16:34, 12 May 2008
(No difference)

Vipul: /* Stronger properties */

2008-03-17T12:48:49Z

Stronger properties

← Older revision		Revision as of 12:48, 17 March 2008
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	===Stronger properties===		===Stronger properties===

			* [[Discrete valuation ring]]

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

Vipul: /* Weaker properties */

2008-03-17T12:48:38Z

Weaker properties

← Older revision		Revision as of 12:48, 17 March 2008
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	* [[Local Cohen-Macaulay ring]]		* [[Local Cohen-Macaulay ring]]
	* [[Local domain]]		* [[Local domain]]
			* [[Unique factorization domain]]
	* [[Integral domain]]: {{proofat\|[[Regular local ring implies integral domain]]}}		* [[Integral domain]]: {{proofat\|[[Regular local ring implies integral domain]]}}

Vipul: /* Weaker properties */

2008-03-10T00:55:47Z

Weaker properties

← Older revision		Revision as of 00:55, 10 March 2008
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	===Weaker properties===		===Weaker properties===

	* [[Local ring]]		* [[Local Cohen-Macaulay ring]]
	* [[Local domain]]		* [[Local domain]]
	* [[Integral domain]]: {{proofat\|[[Regular local ring implies integral domain]]}}		* [[Integral domain]]: {{proofat\|[[Regular local ring implies integral domain]]}}

Vipul: /* Symbol-free definition */

2008-01-05T21:51:08Z

Symbol-free definition

← Older revision		Revision as of 21:51, 5 January 2008
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	===Symbol-free definition===		===Symbol-free definition===

	A [[local ring\|local]] [[commutative unital ring]] is said to be '''regular''' if its unique [[maximal ideal]] is generated (as a module) by as many elements as the [[Krull dimension]] of the ring.		A [[local ring\|local]] [[commutative unital ring]] is said to be '''regular''' if its unique [[maximal ideal]] is generated (as a [[module]] over the ring) by as many elements as the [[Krull dimension]] of the ring.

	==Relation with other properties==		==Relation with other properties==

Vipul at 20:06, 5 January 2008

2008-01-05T20:06:54Z

← Older revision		Revision as of 20:06, 5 January 2008
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	A [[local ring\|local]] [[commutative unital ring]] is said to be '''regular''' if its unique [[maximal ideal]] is generated (as a module) by as many elements as the [[Krull dimension]] of the ring.		A [[local ring\|local]] [[commutative unital ring]] is said to be '''regular''' if its unique [[maximal ideal]] is generated (as a module) by as many elements as the [[Krull dimension]] of the ring.

			==Relation with other properties==

			===Stronger properties===

			===Weaker properties===

			* [[Local ring]]
			* [[Local domain]]
			* [[Integral domain]]: {{proofat\|[[Regular local ring implies integral domain]]}}

Vipul at 11:25, 7 August 2007

2007-08-07T11:25:13Z

New page

{{local ring property}}

==Definition==

===Symbol-free definition===

A [[local ring|local]] [[commutative unital ring]] is said to be '''regular''' if its unique [[maximal ideal]] is generated (as a module) by as many elements as the [[Krull dimension]] of the ring.