cofinitely weak generalized δ-supplemented modules

We will study modules whose cofinite submodules have weak generalized-δ-supplements. we attempt to investigate some properties of cofinitely weak generalized δ-supplemented modules. we will prove for a module m and a semi-δ-hollow submodule n of m that, m is cofinitely weak generalized δ-supplemented if and only if m/n is cofinitely weak generalized δ-supplemented. also we show that any m-generated module is cofinitely weak generalized δ-supplemented module, where m is cofinitely weak generalized δ-supplemented. we obtain some other results about this kind of modules.