Artinian 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

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.

Relation with other properties

Stronger properties

• Field

Weaker properties

• Noetherian ring
• Zero-dimensional ring