Normal ring: Difference between revisions

Revision as of 23:09, 7 January 2008

This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
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VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions

Definition

A commutative unital ring is said to be normal if it is a reduced ring and further, if it is 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.

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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]].