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

• Journal title : Kyungpook mathematical journal
• Volume 54, Issue 4,  2014, pp.587-593
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2014.54.4.587
Title & Authors
The *-Nagata Ring of almost Prüfer *-multiplication Domains
Lim, Jung Wook;

Abstract
Let D be an integral domain with quotient field K, $\small{\bar{D}}$ 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 $\small{D[X]{\subseteq}\bar{D}[X]}$ is a root extension if and only if the *-Nagata ring $\small{D[X]_{N_*}}$ is an AB-domain, if and only if $\small{D[X]_{N_*}}$ 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$\small{\ddot{u}}$fer *-multiplication domain;Pr$\small{\ddot{u}}$fer *-multiplication domain;
Language
English
Cited by
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