Fuzzy semistar operations on overrings

In this paper, we reinvestigate the notion of fuzzy semistar operation introduced in [5]. We show how a fuzzy semistar operation on an integral domain R induces canonically a fuzzy semistar operation on an overring T of R and conversely how a fuzzy semistar operation on T induces canonically a semistar operation on R. As an application, new characterizations of Prüfer domains and complete description of the set of all fuzzy semistar operations of finite character on Prüfer domains are obtained. We also characterize conducive domains.