Bezout ring

This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
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 commutative unital ring (or any commutative ring) is termed a Bezout ring if any finitely generated ideal in it is principal.

Definition with symbols

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Relation with other properties

Stronger properties

• Principal ideal ring

Relation with other properties

• Bezout domain is a Bezout ring that is also an integral domain