UFD (Unique Factorization Domain)
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
integral domain |
| gptkbp:abbreviation |
gptkb:Unique_Factorization_Domain
|
| gptkbp:definedIn |
existence and uniqueness of factorization into irreducibles
|
| gptkbp:example |
Gaussian integers
polynomial ring over a field ring of integers ring of integers of some quadratic fields |
| gptkbp:generalizes |
gptkb:GCD_domain
gptkb:Krull_domain Euclidean domain principal ideal domain |
| gptkbp:hasProperty |
every nonzero non-unit element can be written as a product of irreducible elements
factorization into irreducibles is unique up to order and units every irreducible is prime |
| https://www.w3.org/2000/01/rdf-schema#label |
UFD (Unique Factorization Domain)
|
| gptkbp:implies |
integral domain
atomic domain |
| gptkbp:namedFor |
unique factorization property
|
| gptkbp:studiedIn |
gptkb:commutative_algebra
algebraic number theory |
| gptkbp:bfsParent |
gptkb:commutative_algebra
|
| gptkbp:bfsLayer |
5
|