Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1993-1132407-8
MathSciNet review: 1132407
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16U30

Retrieve articles in all journals with MSC: 16U30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1132407-8
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society