Coherent ring: Difference between revisions
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* Every [[finitely generated module]] over it is [[finitely presented module|finitely presented]] | * Every [[finitely generated module]] over it is [[finitely presented module|finitely presented]] | ||
* Every [[finitely generated ideal]] over it is [[finitely presented ideal|finitely presented]] | * Every [[finitely generated ideal]] over it is [[finitely presented ideal|finitely presented]] | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Noetherian ring]] | |||
Revision as of 00:30, 8 January 2008
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