Artinian ring: Difference between revisions
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==Definition | {{commring property}} | ||
==Definition== | |||
===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[commutative unital ring]] | A [[commutative unital ring]] is termed '''Artinian''' if it satisfies the [[descending chain condition]] on [[ideal]]s, that is, any descending chain of ideals stabilizes after a finite length. | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Field]] | |||
=== | ===Weaker properties=== | ||
* [[Noetherian ring]] | |||
* [[Zero-dimensional ring]] | |||
Revision as of 15:36, 30 June 2007
This article defines a property of commutative rings
Definition
Symbol-free definition
A commutative unital ring is termed Artinian if it satisfies the descending chain condition on ideals, that is, any descending chain of ideals stabilizes after a finite length.