On cofinitely weak $\delta-$ supplemented modules

Let R be a ring and M be a left R- module. M is called cofinitely weak δ-supplemented (or briefly δ- CWS-module) if every cofinite submodule of M has a weak δ-supplement in M. In this paper, we give various properties of this kind of modules. It is shown that a module M is 1-CWS-module if and only if every maximal submodule has a weak δ-supplement in M. The class of cofinitely weak δ-supplemented modules are closed under taking homomorphic images, arbitrary sums and short exact sequences. Also we give some conditions equivalent to being a δ-CWS-module for a δ-coatomic module.