Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13.98

Retrieve articles in all journals with MSC: 13.98


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0272780-1
PII: S 0002-9939(1971)0272780-1
Keywords: Valuation, pseudovaluation, Nullstellensatz
Article copyright: © Copyright 1971 American Mathematical Society