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Proceedings of the American Mathematical Society

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

 

 

Valuations and rings of quotients


Author: David E. Brown
Journal: Proc. Amer. Math. Soc. 43 (1974), 277-282
MSC: Primary 13A15
DOI: https://doi.org/10.1090/S0002-9939-1974-0347792-2
MathSciNet review: 0347792
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Abstract: Valuations on a commutative ring, as defined by Manis, are considered in the special case where the domain of the valuation mapping is a ring of quotients of a given ring $ R$. We consider relations between valuation mappings on various rings of quotients of a given ring. It is also shown that if $ K$ is any von Neumann regular ring of quotients of $ R$, then any pair of nonassociates of $ R$ can be separated by valuations on $ K$ if and only if these elements are nonassociates in the integral closure of $ R$ in $ K$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0347792-2
Keywords: Ring of quotients, separation of nonassociates by valuations, $ R$ is close to $ S$
Article copyright: © Copyright 1974 American Mathematical Society