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Pseudo-Integrality

Published online by Cambridge University Press:  20 November 2018

David F. Anderson ,
Evan G. Houston  and
Muhammad Zafrullah
David F. Anderson
Affiliation:
Department of Mathematics University of Tennessee Knoxville, Tennessee 37996-1300
Evan G. Houston
Affiliation:
Department of Mathematics University of North Carolina at Charlotte Charlotte, NC 28223
Muhammad Zafrullah
Affiliation:
Department of Mathematics University of Iowa Iowa City, IA 52242
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Abstract

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Let R be an integral domain. An element u of the quotient field of R is said to be pseudo-integral over R if uIv ⊆ Iv for some nonzero finitely generated ideal I of R. The set of all pseudo-integral elements forms an integrally closed (but not necessarily pseudo-integrally closed) overling R ofR. It is shown that , where X is a family of indeterminates; pseudo-integrality is analyzed in rings of the form D + M; and an example is given to show that pseudo-integrality does not behave well with respect to localization.

Keywords

13G0513B2013F05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 15 - 22
Copyright
Copyright © Canadian Mathematical Society 1991

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