e*-Extending Modules

Hiba R. Baanoon; Wasan Khild

doi:10.24996/ijs.2023.64.9.25

Authors

Hiba R. Baanoon Department of Mathematics, College of science, University of Baghdad, Baghdad, Iraq / Department of Mathematics, College of Education, University of Misan, Misan, Iraq https://orcid.org/0000-0002-8961-5110
Wasan Khild Department of Mathematics, College of science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.9.25

Keywords:

essential submodule, closed submodule, extending modules, e*-essential submodule, e*-closed submodule, e*-extending modules, e*-coclosed submodule

Abstract

This paper aims to introduce the concepts of -closed, -coclosed, and -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.