Unique Factorization in Polynomial Rings with Zero Divisors

2019/06/03 by Anderson, D. D., Edmonds, Ranthony A. C.
#13 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.00522

Abstract

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 R[X] 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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