Totally ⊕ Generalized *Co finitely Supplemented Modules

Let R be an associative ring with identity, and let M be a unital left R-module, M is called totally ⊕generalized *cofinitely supplemented module for short ( T⊕G*CS), if every submodule of M is a ⊕Generalized *cofinitely supplemented ( ⊕G*CS ). In this paper we prove among the results under certain condition the factor module of T⊕ G*CS is T⊕ G*CS and the finite sum of T ⊕G*CS is T ⊕G*CS.