Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON ALMOST PSEUDO-VALUATION DOMAINS

  • Received : 2010.04.28
  • Accepted : 2010.06.07
  • Published : 2010.06.30
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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

References

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