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Unique factorization in the ring R[x]
Published online by Cambridge University Press: 09 April 2009
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.
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- 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
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