On $\boldsymbol{e^{*}}$-supplemented Modules

Abstract

The purpose of this paper is to introduce the concepts of $e^{*}$-supplement submodules, weakly $e^{*}$-supplement submodules, ample $e^{*}$-supplement submodules, co-$e^{*}$essential submodules, $e^{*}$-supple-mented modules, weakly $e^{*}$-supplemented modules, and amply $e^{*}$-supplemented modules as generalizations of the concepts of supplement submodules, weakly supplement submodules, ample supplement submodules, co-essential submodules, supplemented modules, weakly supplemented modules, and amply supplemented modules, respectively. We will prove some properties of these concepts.