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Proceedings of the American Mathematical Society

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

 
 

 

A weak Nullstellensatz for valuations


Author: George M. Bergman
Journal: Proc. Amer. Math. Soc. 28 (1971), 32-38
MSC: Primary 13.98
DOI: https://doi.org/10.1090/S0002-9939-1971-0272780-1
MathSciNet review: 0272780
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Abstract: Given a real-valued pseudovaluation $p$ on a commutative ring $R$, we show how to obtain a valuation $v$ greater than or equal to $p$, and also satisfying certain upper bounds: in particular, if $p(st) = p(s) + p(t)$ for all $s,t \in S,S$ a multiplicative semigroup in $R$, then $v$ can be chosen so that $v(s) = p(s)$ for all $s \in S$.


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Keywords: Valuation, pseudovaluation, Nullstellensatz
Article copyright: © Copyright 1971 American Mathematical Society