Equidimensional 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

A commutative unital ring is said to be equidimensional if it satisfies both the following conditions:

• All its maximal ideals have the same codimension
• All its minimal prime ideals have the same dimension

Relation with other properties

Stronger properties

• Local Cohen-Macaulay ring