Cofinitely generalized _x000E_-supplemented modules

We will study modules whose cofinite submodules have generalized- supplements. We attempt to investigate some properties of cofinitely generalized -supplemented modules. We will prove for a module M and a semi- -hollow submodule N of M that, M is cofinitely generalized -supplemented i MN is cofinitely generalized -supplemented. Also we will prove that any M-generated of a cofinitely generalized -supplemented module M, is again cofinitely generalized -supplemented. We will get some other suitable results about this kind of modules.