(untitled) (JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences, 2018)
A module M is called closed weak g-supplemented if for any closed submodule N of M, there is a submodule K of M such that and (i.e. K is a weak g-supplement of N in M). In this work many various properties of closed weak g-supplemented modules are investigated. We will prove a module M is closed weak g-supplemented if and only if is closed weak g-supplemented for any closed submodule X of M. So, any direct summand of closed weak g-supplemented module is also closed weak g-supplemented. Every nonsingular homomorphic image of a closed weak g-supplemented module is closed weak g-supplemented. We define and study also modules, in which every cofinite closed submodule of it have weak g-supplements, namely, cofinitely closed weak g-supplemented.