Noun
unique factorization domain (plural unique factorization domains)
(algebra, ring theory) A unique factorization ring which is also an integral domain.
Any Euclidean domain is a unique factorization domain (UFD), although the converse is not true. Source: Internet
A unique factorization domain is not necessarily a noetherian ring. Source: Internet
In a unique factorization domain (or more generally, a GCD domain ), an irreducible element is a prime element. Source: Internet
This paper not only introduced the Gaussian integers and proved they are a unique factorization domain, it also introduced the terms norm, unit, primary, and associate, which are now standard in algebraic number theory. Source: Internet