Bezout domain: Difference between revisions
No edit summary |
No edit summary |
||
| Line 6: | Line 6: | ||
An [[integral domain]] is termed a '''Bezout domain''' if every [[finitely generated ideal]] in it is [[principal ideal|principal]]. | An [[integral domain]] is termed a '''Bezout domain''' if every [[finitely generated ideal]] in it is [[principal ideal|principal]]. | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Principal ideal domain]] | |||
* [[Multi-stage Euclidean domain]] | |||
===Weaker properties=== | |||
* [[gcd domain]] | |||
Revision as of 23:15, 16 December 2007
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.