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On complete integral closure and Archimedean valuation domains

Part of: Ring extensions and related topics Integral domains General commutative ring theory

Published online by Cambridge University Press:  09 April 2009

Robert Gilmer
Robert Gilmer
Affiliation:
Florida State University Tallahassee, FL 32306-3027 USA e-mail: [email protected]
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Abstract

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Suppose D is an integral domain with quotient field K and that L is an extension field of K. We show in Theorem 4 that if the complete integral closure of D is an intersection of Archimedean valuation domains on K, then the complete integral closure of D in L is an intersection of Archimedean valuation domains on L; this answers a question raised by Gilmer and Heinzer in 1965.

MSC classification

Secondary: 13A18: Valuations and their generalizations 13B02: Extension theory 13B22: Integral closure of rings and ideals ; integrally closed rings, related rings (Japanese, etc.) 13G05: Integral domains
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 3 , December 1996 , pp. 377 - 380
Copyright
Copyright © Australian Mathematical Society 1996

References

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