Noetherian local ring

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

Definition

A Noetherian local ring (or local Noetherian ring) is a commutative unital ring that is both a Noetherian ring (i.e. every ideal is finitely generated) and a local ring (i.e. there is a unique maximal ideal).

Relation with other properties

Stronger properties

• Regular local ring
• Local Cohen-Macaulay ring
• Local Artinian ring
• Local Noetherian domain