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http://dx.doi.org/10.5666/KMJ.2014.54.4.587

The *-Nagata Ring of almost Prüfer *-multiplication Domains  

Lim, Jung Wook (Department of Mathematics, Kyungpook National University)
Publication Information
Kyungpook Mathematical Journal / v.54, no.4, 2014 , pp. 587-593 More about this Journal
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.
Keywords
*-Nagata ring; almost Pr$\ddot{u}$fer *-multiplication domain; Pr$\ddot{u}$fer *-multiplication domain;
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