Cofinitely Rationally Closed Weak Supplemented Modules

Authors

  • Mahdi Saleh Nayef Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq
  • Zahraa Abbas Fadel Third karkh education directorate, Ministry of Education, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2024.65.12.25

Keywords:

Cofinitely rationally closed weak supplemented module, cofinite rationally closed submodule, closed cofinitely weak supplemented module

Abstract

The module  is cofinitely rationally closed weak supplemented module (denoted by CRCWS-module) if every cofinite rationally closed submodule of  has weak supplement submodule in . The CRCWS- module is stronger generalize of closed cofinitely weak supplemented modules. In addition, we present a rationally closed weak supplemented modules (denoted by RCWS-module) which is a stronger generalize of closed weak supplemented modules. The relationships of our concepts to other related concepts was discussed and studied, and we give the conditions that make them equivalent were given. And also, we gave the necessary condition that makes the direct sum of RCWS-module (or CRCWS-module) is RCWS-module (CRCWS-module).

 

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Published

2024-12-30

Issue

Section

Mathematics

How to Cite

Cofinitely Rationally Closed Weak Supplemented Modules. (2024). Iraqi Journal of Science, 65(12), 7109-7116. https://doi.org/10.24996/ijs.2024.65.12.25