Regular ring: Difference between revisions
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A [[commutative unital ring]] is termed a '''regular ring''' if its [[localization at a prime ideal|localization at any prime ideal]] is a [[regular local ring]]. | A [[commutative unital ring]] is termed a '''regular ring''' if its [[localization at a prime ideal|localization at any prime ideal]] is a [[regular local ring]]. | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Regular local ring]] | |||
===Weaker properties=== | |||
* [[Cohen-Macaulay ring]] | |||
* [[Universally catenary ring]] | |||
* [[Catenary ring]] | |||
* [[Noetherian ring]] | |||
==External links== | ==External links== | ||
===Definition links=== | ===Definition links=== | ||
* {{mathworld|RegularRing}} | * {{mathworld|RegularRing}} | ||
Revision as of 22:11, 9 March 2008
This is not to be confused with von-Neumann regular ring
This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
View all properties of commutative unital rings
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 termed a regular ring if its localization at any prime ideal is a regular local ring.