The *-Nagata Ring of almost Prufer *-multiplication Domains
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Let D be an integral domain with quotient field K, 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] ⊆ D￣[X] is a root extensionif 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.
Abstract
Let D be an integral domain with quotient field K, 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] ⊆ D￣[X] is a root extensionif 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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