Unique factorization domain
INTEGRAL DOMAIN WHERE EVERY NONZERO ELEMENT IS UNIQUELY EXPRESSIBLE AS A PRODUCT OF PRIME ELEMENTS
Unique factorization; Factorial ring; Unique factorisation; Unique factorisation domain; Unique Factorization Domain; Factorial domain; UFD (math)
In mathematics, a unique factorization domain (UFD) (also sometimes called a factorial ring following the terminology of Bourbaki) is a ring in which a statement analogous to the fundamental theorem of arithmetic holds. Specifically, a UFD is an integral domain (a nontrivial commutative ring in which the product of any two non-zero elements is non-zero) in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units.