A generalization of cofinitely weak rad-supplemented modules

We say that a module M is a closed cofinitely weak generalized supplemented module or briefly ccwgs-module if for every N ≤ cc M, N has a weak Rad-supplement in M. In this article, the various properties of ccwgs-modules are given as a proper generalization of cofinitely weak Rad-supplemented modules. We prove that every cofinite direct sum of a ccwgs-module is a ccwgs-module. In particular, we also prove that every ccwgs-module over a left Bass ring is a ccws-module. Finally, we show that the notion of cofinitely weak Rad-supplemented modules and the notion of ccwgs-modules are equivalent under some special conditions.