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Unique factorization in the ring R[x]

Part of: Rings and algebras arising under various constructions Conditions on elements

Published online by Cambridge University Press:  09 April 2009

Raymond A. Beauregard
Raymond A. Beauregard
Affiliation:
University of Rhode IslandKingston, R.I. 02881, USA
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Abstract

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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.

MSC classification

Secondary: 16U30: Divisibility, noncommutative UFDs 16S36: Ordinary and skew polynomial rings and semigroup rings

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 3 , December 1992 , pp. 287 - 293
Copyright
Copyright © Australian Mathematical Society 1992

References

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