Duals and Transforms of Ideals in PVMDs

Abstract

In this paper we study when the dual of a $t$-ideal in a $PVMD$ is a ring? and we treat the question when it coincides with its endomorphism ring. We also study particular classes of overrings of PVMDs. Specially, we investigate the Nagata transform and the endomorphism ring of ideals in PVMDs in an attempt to establish analogues for well-known results on overrings of Pr\"ufer domains.