Valuations and rings of quotients

Brown, David E.

doi:10.1090/S0002-9939-1974-0347792-2

Valuations and rings of quotients
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by David E. Brown

Proc. Amer. Math. Soc. 43 (1974), 277-282

DOI: https://doi.org/10.1090/S0002-9939-1974-0347792-2

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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 $K$.

References

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