Fuzzy semistar operations on overrings

摘要

AbstractIn this paper, we reinvestigate the notion of fuzzy semistar operation introduced in . We show how a fuzzy semistar operation on an integral domainRinduces canonically a fuzzy semistar operation on an overringTofRand conversely how a fuzzy semistar operation onTinduces canonically a semistar operation onR. 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.