Coherent 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 coherent if it satisfies the following equivalent conditions:

• Every finitely generated module over it is finitely presented
• Every finitely generated ideal over it is finitely presented

Relation with other properties

Stronger properties

• Noetherian ring