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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Integrally closed subrings of an integral domain


Authors: Robert Gilmer and Joe Mott
Journal: Trans. Amer. Math. Soc. 154 (1971), 239-250
MSC: Primary 13.15
MathSciNet review: 0271082
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Abstract: Let D be an integral domain with identity having quotient field K. This paper gives necessary and sufficient conditions on D in order that each integrally closed subring of D should belong to some subclass of the class of integrally closed domains; some of the subclasses considered are the completely integrally closed domains, Prüfer domains, and Dedekind domains.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0271082-1
Keywords: Integrally closed domain, completely integrally closed, Prüfer domain, Krull domain, Dedekind domain, almost Dedekind domain
Article copyright: © Copyright 1971 American Mathematical Society