Local Noetherian domain

This article defines a property of integral domains, viz., a property that, given any integral domain, is either true or false for that.
View other properties of integral domains | 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

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

Definition

A local Noetherian domain is a commutative unital ring that is all of these: a Noetherian ring, a local ring, and an integral domain.

Relation with other properties

Stronger properties

• Regular local ring
• Local Cohen-Macaulay domain

Weaker properties

• Equidimensional ring: For full proof, refer: Local Noetherian domain implies equidimensional
• Local domain
• Noetherian domain
• Local Noetherian ring