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An Analog of Nagata's Theorem for Modular LCM Domains
Published online by Cambridge University Press: 20 November 2018
Abstract
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]).
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- Copyright © Canadian Mathematical Society 1977
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