Unique factorization domain

GPTKB entity

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
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:Euclidean_domain gptkb:GCD_domain gptkb:Irreducible_element gptkb:Principal_ideal_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:Integral_domain gptkb:Irreducible_element gptkb:Principal_ideal_domain
gptkbp:bfsLayer	8
https://www.w3.org/2000/01/rdf-schema#label	Unique factorization domain