Modules having (weak-s*)‎ property

الملخص EN

Let R be a non-zero ring with identity and let Me 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 sub module N of M contains a direct summand K of M such that K ≤ N and N / K is weak-cosingular.

And we study the properties of this kind of modules, and the relation between this modules and other kind of modules.