Normal ring - Revision history

Vipul: /* Metaproperties */

2009-02-07T02:31:47Z

Metaproperties

← Older revision		Revision as of 02:31, 7 February 2009
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	{{localization-closed curing property}}		{{localization-closed curing property}}

	The localization of a normal ring at any multiplicatively closed subset not containing zero, and hence, in particular, the localization relative to any prime ideal, is again a normal ring.		The localization of a normal ring at any multiplicatively closed subset not containing zero, and hence, in particular, the localization relative to any prime ideal, is again a normal ring. {{proofat\|[[Normality is localization-closed]]}}

			{{poly-closed curing property}}

			The polynomial ring over a normal ring is a normal ring. {{proofat\|[[Normality is polynomial-closed]]}}

Vipul: 3 revisions

2008-05-12T16:28:15Z

3 revisions

← Older revision	Revision as of 16:28, 12 May 2008
(No difference)

Vipul at 23:17, 15 March 2008

2008-03-15T23:17:42Z

← Older revision		Revision as of 23:17, 15 March 2008
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	This generalizes the notion of [[normal domain]] where we require the [[integral domain]] to be integrally closed in its [[field of fractions]].		This generalizes the notion of [[normal domain]] where we require the [[integral domain]] to be integrally closed in its [[field of fractions]].

			==Relation with other properties==

			==Metaproperties==

			{{localization-closed curing property}}

			The localization of a normal ring at any multiplicatively closed subset not containing zero, and hence, in particular, the localization relative to any prime ideal, is again a normal ring.

Vipul at 23:09, 7 January 2008

2008-01-07T23:09:45Z

← Older revision		Revision as of 23:09, 7 January 2008
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	A [[commutative unital ring]] is said to be '''normal''' if it is a [[reduced ring]] and further, if it is [[integrally closed subring\|integrally closed]] in its [[total quotient ring]].		A [[commutative unital ring]] is said to be '''normal''' if it is a [[reduced ring]] and further, if it is [[integrally closed subring\|integrally closed]] in its [[total quotient ring]].

	This generalizes the notion of normal domain where we require the [[integral domain]] to be integrally closed in its [[field of fractions]].		This generalizes the notion of [[normal domain]] where we require the [[integral domain]] to be integrally closed in its [[field of fractions]].

Vipul at 07:18, 9 August 2007

2007-08-09T07:18:00Z

New page

{{curing property}}

==Definition==

A [[commutative unital ring]] is said to be '''normal''' if it is a [[reduced ring]] and further, if it is [[integrally closed subring|integrally closed]] in its [[total quotient ring]].

This generalizes the notion of normal domain where we require the [[integral domain]] to be integrally closed in its [[field of fractions]].