Abstract
The purpose of this paper is to introduce a new concept in a module M over a ring R, this concept is called e∗-essential submodule, which is a generalization of an essential submodule. We will introduce some examples and properties about this concept such that, what is the inverse image of e∗-essential submodule, the intersection of e∗-essential submodules and direct sum of e∗-essential submodules. We will show the relationship between e∗-essential submodule and Noetherian R-module. Also we will define e∗-closed submodule with some properties
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