Unique factorization rings

Abstract

1. The concept of a unique factorization domain (UFD) has been defined, for commutative (e.g. (4) page 21) and non-commutative (1) integral domains. We take the theory a stage further here by defining a unique factorization ring (UFR), where throughout, a ring is understood to mean a commutative ring with identity, possibly containing proper zero-divisors.