FI-Rad_J-Supplemented and FI-⨁-Rad_J-Supplemented Modules

Abdulkareem Ali; Hiba R.  Baanoon

doi:10.24996/ijs.2025.66.4.%g

Authors

Abdulkareem Ali Department of Mathematics, College of Education, University of Misan, Misan, IRAQ https://orcid.org/0009-0004-3733-7077
Hiba R. Baanoon Department of Mathematics, College of Education, University of Misan, Misan, IRAQ

DOI:

https://doi.org/10.24996/ijs.2025.66.4.%25g

Keywords:

Supplemented Modules, Weakly Supplemented Modules, ⨁-Supplemented Modules, Rad_J-Supplemented Modules, ⨁-Rad_J-Supplemented Modules

Abstract

Assume that R is any ring with identity and M is a unitary left R-module. This work introduces the Rad_J-Supplemented module with respect to the fully invariant submodule it is denoted by (FI-Rad_J-Supplemented) and ⨁-Rad_J-Supplemented modules with respect to the fully invariant submodule (denoted by FI-⨁-Rad_J-Supplemented modules). As well as the main features of these modules in this work, and various properties of these modules. Also, we defined weakly FI-Rad_J-Supplemented modules as an extension of the FI-Rad_J-supplemented modules and we explain the relationship between them using notes and examples.