Noetherian UFD

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

Definition

Symbol-free definition

A Noetherian UFD is an integral domain which satisfies the following equivalent conditions:

• It is Noetherian and a unique factorization domain
• Every prime ideal minimal over a principal ideal is itself principal

Relation with other properties

Stronger properties

• Principal ideal domain

Weaker properties

• Noetherian normal domain