Korean Journal of Mathematics

  • 제18권2호
  • /
  • Pages.185-193
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  • 2010
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지

ON ALMOST PSEUDO-VALUATION DOMAINS

  • 투고 : 2010.04.28
  • 심사 : 2010.06.07
  • 발행 : 2010.06.30
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⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

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