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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
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$.

References [Enhancements On Off] (What's this?)

  • [1] P. M. Cohn, An invariant characterization of pseudo-valuations on a field, Proc. Cambridge Philos. Soc. 50 (1954), 159–177. MR 0064027

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