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ON ALMOST PSEUDO-VALUATION DOMAINS  

Chang, Gyu Whan (Department of Mathematics University of Incheon)
Publication Information
Korean Journal of Mathematics / v.18, no.2, 2010 , pp. 185-193 More about this Journal
Abstract
Let D be an integral domain, and let ${\bar{D}}$ be the integral closure of D. We show that if D is an almost pseudo-valuation domain (APVD), then D is a quasi-$Pr{\ddot{u}}fer$ domain if and only if D=P is a quasi-$Pr{\ddot{u}}fer$ domain for each prime ideal P of D, if and only if ${\bar{D}}$ is a valuation domain. We also show that D(X), the Nagata ring of D, is a locally APVD if and only if D is a locally APVD and ${\bar{D}}$ is a $Pr{\ddot{u}}fer$ domain.
Keywords
almost pseudo-valuation domain (APVD); locally APVD; quasi-$Pr{\ddot{u}}fer$ domain; D(X);
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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