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An Analog of Nagata's Theorem for Modular LCM Domains

Published online by Cambridge University Press:  20 November 2018

Raymond A. Beauregard
Raymond A. Beauregard*
Affiliation:
University of Rhode Island, Kingston, Rhode Island
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Abstract

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The theorem referred to in the title asserts that for an atomic commutative integral domain R, if S is a submonoid of R* (the monoid of nonzero elements of R) generated by primes such that the quotient ring RS-1 is a UFD (unique factorization domain) then R is also a UFD [8]. Recently several definitions of a noncommutative UFD have been proposed (see the summary in [6]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 307 - 314
Copyright
Copyright © Canadian Mathematical Society 1977

References

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