Modules whose fully invariant ec-closed submodules are direct summands

Abstract

In this article, we define a module H to be fully invariant ECS-module if and only if for each fully invariant ec-closed submodule of H is a direct summand. We investigate fully invariant ECS-modules and locate this property among the other generalizations of the CS notion. This new class of modules is a proper generalization of each of fully invariant extending and ECS-modules. It is well known that the class of ECS-modules is not closed under direct sums, while in this paper, we show that fully invariant ECS-modules are closed under direct sums.