= Noncommutative unique factorization domain
{wiki=Noncommutative_unique_factorization_domain}
A **noncommutative unique factorization domain (UFD)** is a generalization of the concept of a unique factorization domain in commutative algebra, extended to the realm of noncommutative algebra. In the context of commutative algebra, a unique factorization domain is an integral domain in which every non-zero non-unit element can be factored uniquely (up to order and units) into irreducible elements.
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