Goldie Rationally Extending Modules

Mahdi Saleh Nayef; Zahraa Abbas Fadel

doi:10.24996/ijs.2023.64.11.25

Authors

Mahdi Saleh Nayef Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq
Zahraa Abbas Fadel Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0003-0589-3859

DOI:

https://doi.org/10.24996/ijs.2023.64.11.25

Keywords:

Rationally Extending Modules, Goldie Rationally Extending Modules, Goldie Extending Modules

Abstract

In this work, we introduce a new generalization of both Rationally extending and Goldie extending which is Goldie Rationally extending module which is known as follows: if for any submodule K of an R-module M there is a direct summand U of M (denoted by U⊆_⊕ M) such that K β_r U. A β_r is a relation of K⊆M and U⊆M, which defined as K β_r U if and only if K ⋂U⊆_r K and K⋂U⊆_r U.