Regular local ring

This article defines a property that can be evaluated for a local ring
View other properties of local rings

Definition

Symbol-free definition

A local commutative unital ring is said to be regular if its unique maximal ideal is generated (as a module over the ring) by as many elements as the Krull dimension of the ring.

Relation with other properties

Stronger properties

• Discrete valuation ring

Weaker properties

• Local Cohen-Macaulay ring
• Local domain
• Unique factorization domain
• Integral domain: For full proof, refer: Regular local ring implies integral domain