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When is $ F[x,y]$ a unique factorization domain?

Author: Raymond A. Beauregard
Journal: Proc. Amer. Math. Soc. 117 (1993), 67-70
MSC: Primary 16U30
MathSciNet review: 1132407
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Abstract: Although the commutative polynomial ring $ F[x,y]$ is a unique factorization domain (UFD) and the free associative algebra $ F\langle x,y\rangle $ is a similarity-UFD when $ F$ is a (commutative) field, it is shown that the polynomial ring $ F[x,y]$ in two commuting indeterminates is not a UFD in any reasonable sense when $ F$ is the skew field of rational quaternions.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1993 American Mathematical Society