Crossref Citations
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Smertnig, Daniel
2016.
Multiplicative Ideal Theory and Factorization Theory.
Vol. 170,
Issue. ,
p.
353.
Published online by Cambridge University Press: 09 April 2009
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.