F-J-semi Regular Modules

Abstract

Let be a ring with identity and let be a left R-module. If is a proper submodule of and , is called --semi regular element in , If there exists a decoposition such that is projective submodule of and . The aim of this paper is to introduce properties of F-J-semi regular module. In particular, its characterizations are given. Furthermore, we introduce the concepts of Jacobson hollow semi regular module and --semiregular module. Finally, many results of Jacobson hollow semi regular module and --semiregular module are presented.