Cohen-Macaulay 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 Cohen-Macaulay if it satisfies the following equivalent conditions:
- For any maximal ideal, the depth equals the codimension
- For any prime ideal, the depth equals the codimension
- For any ideal, the depth equals the codimension