Closed weak G-supplemented modules

Abstract EN

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.