In this work, cofinitely (weak) g-supplemented lattices are defined and some properties of these investigated. It is shown that quotient sublattices g-supplemented. If 〖{a_i/0} 〗_(i∈I) a collection L 1=⋁_(i∈I) a_i, then also proved without loss generality weak g-supplements cofinite elements in compactly generated compact. An example showing not true for which given. A condition given under lat...

The aim of this paper is to investigate strong notion strongly ⨁-supplemented modules in module theory, namely ⨁-locally artinian supplemented modules. We call a M if it locally and its supplement submodules are direct summand. In study, we provide the basic properties particular, show that every summand supplemented. Moreover, prove ring R semiperfect with radical only projective R-module

In this paper, we introduce the concept of (amply) cofinitely ss-supplemented modules as a proper generalization modules, and provide various properties these modules. particular, prove that arbitrary sum is ss-supplemented. Moreover, show ring R semiperfect Rad(R)⊆Soc(RR) if only every left R-module