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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

An integrally closed ring which is not the intersection of valuation rings


Author: Joachim Gräter
Journal: Proc. Amer. Math. Soc. 107 (1989), 333-336
MSC: Primary 13B20; Secondary 13A18
MathSciNet review: 972231
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Abstract: Each commutative ring $ R$ which is integrally closed in its total quotient ring $ T(R)$ is the intersection of all paravaluation rings of $ T(R)$ containing $ R$. In this note an example is given that shows that this statement is not true with "valuation rings" instead of "paravaluation rings". This is an answer of a question asked by J. A. Huckaba in [3].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0972231-9
PII: S 0002-9939(1989)0972231-9
Keywords: Commutative rings, integral closure, valuation rings
Article copyright: © Copyright 1989 American Mathematical Society