Local 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 domain is a local ring which is also an integral domain.

Relation with other properties

Stronger properties

• Regular local ring: For full proof, refer: Regular local ring implies integral domain
• Local Noetherian domain
• Field

Weaker properties

• Local ring
• Integral domain