Given a certain factorization property of a ring R, we can ask if this property extends to the polynomial ring over R or vice versa. For example, it is well known that R is a unique factorization domain if and only if RX is a unique factorization domain. If R is not a domain, this is no longer true. In this paper, we survey unique factorization in commutative rings with zero divisors, and characterize when a polynomial ring over an arbitrary commutative ring has unique factorization.
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