J Austral Math Soc Ser A 53 pp287--293, 1992.

Unique Factorization in the Ring R[x]

Raymond A. Beauregard

Abstract

If R is a commutative unique factorization domain (UFD) then so is the ring R[x]. If R is not commutative then no such result is possible. An example is given of a bounded principal right and left ideal domain R, hence a similarity-UFD, for which the polynomial ring R[x] in a central indeterminate x is not a UFD in any reasonable sense. On the other hand, it is shown that if R is an invariant UFD then R[x] is a UFD in an appropriate sense.

1991 AMS Subject Classification: 16A02, 16A05, 16U30, 16S36

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Authors

Raymond A. Beauregard

University of Rhode Island, Kinhston, R.I. 02881, USA.