Bezout domain

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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

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Euclidean domain admits a Euclidean norm click here
Principal ideal domain every ideal is a principal ideal click here
Multi-stage Euclidean domain click here

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
gcd domain any two elements have a well-defined gcd Bezout implies gcd gcd not implies Bezout click here
Bezout ring click here

Conjunction with other properties