The *-Nagata ring of almost Prüfer *-multiplication domains

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 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.