MODULES HAVING (WEAK-S*) PROPERTY

Let R be a non zero ring with identity and let M be a non zero module over R. An R-module M is called cosingular if Z*(M)=M where Z*(M)={m ∈ M, mR E(M)}, in this paper we introduce the concept that an R-module M is weak-cosingular if Z*(M)≤e M. and we call that an R-module has (weak-S*)property if every submodule N of M contains a direct summand K of M such that K≤N and N/K is weakcosingular. an‎d we study the properties of this kind of modules, and the relation between this modules and other kind of modules.