e∗-Extending Modules

Abstract

This paper aims to introduce the concepts of e∗-closed, e∗-coclosed, and e∗extending modules as generalizations of the closed, coclossed, and extending modules, respectively. We will prove some properties as when the image of the e*closed submodule is also e*-closed and when the submodule of the e*-extending module is e*-extending. Under isomorphism, the e*-extending modules are closed. We will study the quotient of e*-closed and e*-extending, the direct sum of e*closed, and the direct sum of e*-extending.