Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:King
|
| gptkbp:defines |
A ring in which every finitely generated ideal is principal
|
| gptkbp:example |
The ring of entire functions is a Bézout ring
The ring of integers is a Bézout ring The ring of polynomials in one variable over a field is a Bézout ring |
| gptkbp:fieldOfStudy |
gptkb:commutative_algebra
abstract algebra |
| gptkbp:generalizes |
principal ideal domain
Bézout domain |
| https://www.w3.org/2000/01/rdf-schema#label |
Bézout ring
|
| gptkbp:namedAfter |
gptkb:Étienne_Bézout
|
| gptkbp:property |
A Bézout ring need not be Noetherian
A Bézout ring need not be a domain A Bézout ring need not be a principal ideal ring Every Bézout domain is a Bézout ring Every principal ideal ring is a Bézout ring |
| gptkbp:relatedTo |
gptkb:Bézout's_identity
commutative ring Bézout domain principal ideal ring |
| gptkbp:bfsParent |
gptkb:Étienne_Bézout
|
| gptkbp:bfsLayer |
6
|