Bezout domain: Difference between revisions
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Principal ideal domain]] | * [[Weaker than::Euclidean domain]] | ||
* [[Multi-stage Euclidean domain]] | * [[Weaker than::Principal ideal domain]] | ||
* [[Weaker than::Multi-stage Euclidean domain]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
* [[gcd domain]]: {{proofofstrictimplicationat|[[Bezout implies gcd]]|[[gcd not implies Bezout]]}} | * [[Stronger than::gcd domain]]: {{proofofstrictimplicationat|[[Bezout implies gcd]]|[[gcd not implies Bezout]]}} | ||
Revision as of 17:18, 17 January 2009
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
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