Cohen-Macaulay ideal

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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 outside


View 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.

Relation with other properties

Stronger properties

In particular kinds of rings

In affine rings