Noetherian local ring: Difference between revisions
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==Definition== | |||
A '''Noetherian local ring''' (or '''local Noetherian ring''') is a [[commutative unital ring]] that is both a [[Noetherian ring]] (i.e. every ideal is finitely generated) ''and'' a [[local ring]] (i.e. there is a unique [[maximal ideal]]). | |||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Regular local ring]] | |||
* [[Local Cohen-Macaulay ring]] | |||
* [[Local Artinian domain]] | |||
* [[Local Noetherian domain]] | |||
Revision as of 00:25, 17 March 2008
This article defines a property that can be evaluated for a local ring
View other properties of local rings
Definition
A Noetherian local ring (or local Noetherian ring) is a commutative unital ring that is both a Noetherian ring (i.e. every ideal is finitely generated) and a local ring (i.e. there is a unique maximal ideal).