e*-Extending Modules
DOI:
https://doi.org/10.24996/ijs.2023.64.9.25Keywords:
essential submodule, closed submodule, extending modules, e*-essential submodule, e*-closed submodule, e*-extending modules, e*-coclosed submoduleAbstract
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.