Bezout 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

Definition

Symbol-free definition

An integral domain is termed a Bezout domain if every finitely generated ideal in it is principal.

Relation with other properties

Stronger properties

• Euclidean domain
• Principal ideal domain
• Multi-stage Euclidean domain

Weaker properties

• gcd domain: For proof of the implication, refer Bezout implies gcd and for proof of its strictness (i.e. the reverse implication being false) refer gcd not implies Bezout
• Bezout ring

Conjunction with other properties

• Principal ideal domain is the conjunction with the property of being a Noetherian ring.