Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:abbreviation |
gptkb:UFD
|
| gptkbp:defines |
An integral domain in which every nonzero nonunit element can be written as a product of irreducible elements, uniquely up to order and units.
|
| gptkbp:example |
The polynomial ring k[x] over a field k is a unique factorization domain.
The ring of integers Z is a unique factorization domain. The ring Z[√-5] is not a unique factorization domain. |
| gptkbp:field |
gptkb:Abstract_algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
Unique Factorization Domain
|
| gptkbp:introduced |
gptkb:Richard_Dedekind
|
| gptkbp:introducedIn |
19th century
|
| gptkbp:isA |
gptkb:Integral_domain
|
| gptkbp:property |
Every unique factorization domain is a GCD domain.
Every principal ideal domain is a unique factorization domain. |
| gptkbp:relatedConcept |
gptkb:GCD_domain
gptkb:Irreducible_element gptkb:Principal_ideal_domain Euclidean domain Prime element |
| gptkbp:bfsParent |
gptkb:UFD_(Unique_Factorization_Domain)
|
| gptkbp:bfsLayer |
6
|