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 MN 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. 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 MN 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.