Supplement Continuous and Quasi-Supplement Continuous Modules

Sarah Hassan Ali; Mahdi Saleh  Nayef

doi:10.24996/ijs.2024.65.10.24

Authors

Sarah Hassan Ali Department of Mathematics, College of Education, AL- Mustansiriyah University, Baghdad, Iraq https://orcid.org/0009-0006-1796-7279
Mahdi Saleh Nayef Department of Mathematics, College of Education, AL- Mustansiriyah University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2024.65.10.24

Keywords:

Extending Modules, Supplement Extending Modules, P_1-Modules, P_2-Modules, P_3-module, supplement continuous Modules, quasi-supplement continuous Modules

Abstract

In this research, we introduce the concepts of -module where (i=1,2,3), as proper generalizations of -conditions, where (i=1,2,3). The relationships between these concepts and previous ones were explained, and a comprehensive description of each was provided. Additionally, by relying on -module, new concepts were developed, such as supplement continuous and quasi-supplement continuous, which represent generalizations of continuous and quasi-continuous. Illustrative examples were provided, and the possibility of their inheritance was discussed.