Fuzzy injective S-act on monoids

Abstract

The fuzzy injectivity and their generalizations on R-modules were studied by many authors. It is well known that the act of semigroups or monoids is a generalization of R-modules, here we will define the fuzzy injective S-acts or S-systems and studied some of their properties first we discuss when the subacts of fuzzy S-acts is fuzzy injective S-act , we studied the retracts ,the factor fuzzy injective S-act and finally we studied their direct product.