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

Valuation rings with zero divisors


Authors: Patrick H. Kelly and Max D. Larsen
Journal: Proc. Amer. Math. Soc. 30 (1971), 426-430
MSC: Primary 13.98
MathSciNet review: 0285527
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Abstract: Manis has developed a valuation theory for commutative rings which extends valuation theory for fields. However his results do not extend the characterization of valuation rings as domains of maximal partial homomorphisms. In this note we show that Manis' theory also generalizes this aspect of valuation theory. Next we show that an overring W of a valuation ring V is not necessarily a valuation ring in any nice sense, but that W is contained in a valuation ring which is a large quotient ring of V.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0285527-X
PII: S 0002-9939(1971)0285527-X
Keywords: Maximal partial homomorphism, valuation pair, overring of valuation ring
Article copyright: © Copyright 1971 American Mathematical Society