Kyungpook Mathematical Journal

  • 제54권4호
  • /
  • Pages.587-593
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  • 2014
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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The *-Nagata Ring of almost Prüfer *-multiplication Domains

  • Lim, Jung Wook (Department of Mathematics, Kyungpook National University)
  • 투고 : 2014.01.02
  • 심사 : 2014.04.09
  • 발행 : 2014.12.23
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초록

Let D be an integral domain with quotient field K, $\bar{D}$ denote the integral closure of D in K and * be a star-operation on D. In this paper, we study the *-Nagata ring of AP*MDs. More precisely, we show that D is an AP*MD and $D[X]{\subseteq}\bar{D}[X]$ is a root extension if and only if the *-Nagata ring $D[X]_{N_*}$ is an AB-domain, if and only if $D[X]_{N_*}$ is an AP-domain. We also prove that D is a P*MD if and only if D is an integrally closed AP*MD, if and only if D is a root closed AP*MD.

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참고문헌

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피인용 문헌

  1. Semigroup rings as almost Prüfer v-multiplication domains 2017, https://doi.org/10.1007/s00233-017-9898-x