# Cohen-Macaulay ideal

From Commalg

This article is about a definition in group theory that is standard among the commutative algebra community (or sub-community that dabbles in such things) but is not very basic or common for people outsideView a list of other standard non-basic definitions

This article defines a property of an ideal in a commutative unital ring |View other properties of ideals in commutative unital rings

This property of an ideal in a ring is equivalent to the property of the quotient ring being a/an: Cohen-Macaulay ring | View other quotient-determined properties of ideals in commutative unital rings

## Definition

An ideal in a commutative unital ring is termed a **Cohen-Macaulay ideal** if the quotient ring is a Cohen-Macaulay ring.