Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:abbreviation |
gptkb:UFD
|
| gptkbp:defines |
An integral domain in which every nonzero non-unit 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:property |
Every unique factorization domain is a GCD domain.
Every principal ideal domain is a unique factorization domain. Every unique factorization domain is integrally closed. |
| gptkbp:relatedConcept |
gptkb:GCD_domain
gptkb:Irreducible_element gptkb:Principal_ideal_domain Euclidean domain Prime element |
| gptkbp:type |
gptkb:Integral_domain
|
| gptkbp:used_in |
gptkb:Algebraic_geometry
gptkb:Commutative_algebra gptkb:Algebraic_number_theory |
| gptkbp:bfsParent |
gptkb:Prime_decomposition_theorem
gptkb:Divisor_theory gptkb:Integral_domain gptkb:Irreducible_element gptkb:Principal_ideal_domain |
| gptkbp:bfsLayer |
8
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