A note on intersections of valuation ideals

Author:
Charles H. Brase

Journal:
Proc. Amer. Math. Soc. **38** (1973), 37-39

DOI:
https://doi.org/10.1090/S0002-9939-1973-0309915-X

MathSciNet review:
0309915

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Abstract | References | Additional Information

Abstract: In this note it is proved that if is an integral domain the set of valuation ideals of is closed under intersection if and only if the integral closure of is a valuation ring. Let be a domain which is integrally dependent on and contains the integral closure of . Then the set of valuation ideals of is the same as the set of ideals of which contract from ideals of if and only if the set of valuation ideals of is closed under intersection.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0309915-X

Keywords:
Valuation ideal,
completion,
integral closure

Article copyright:
© Copyright 1973
American Mathematical Society