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
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| local Cohen-Macaulay ring | click here | |||
| local Noetherian domain | integral domain with a unique maximal ideal | click here |