A not of Modules with (f.S*) Property

Abstract

Let R be an associative ring with identity and M be unital non zero right R-module. In this work,we introduce (f.S*) property as a generilization of (S*) property .A module M is said to satisfy the property (f.S*) if for every finitely generated submodule N of M there exists a direct summand K of M such that K£N and N/K is cosingular. A ring R satisfies (f.S*) if the (right) R-module R satisfies (f.S*), and study the concept of module that satisfies the property of (f.S*) we was proved in theorem (3.1) that every right R-module M is satisfies (f.S*) if and only if every finitily generated submodule is direct sum of injective module and a cosingular module .Also we investigate some of their properties that are relevant with our work .