Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The *-Nagata Ring of almost Prüfer *-multiplication Domains

  • Lim, Jung Wook (Department of Mathematics, Kyungpook National University)
  • Received : 2014.01.02
  • Accepted : 2014.04.09
  • Published : 2014.12.23
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Abstract

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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