The dual of the notions r-submodules, n-submodules, and J-submodules

TL;DR

This paper introduces and investigates the dual concepts of r-submodules, n-submodules, and J-submodules in R-modules over commutative rings, expanding the theoretical framework of module theory.

Contribution

It presents the first formal definitions and properties of the dual notions of r-, n-, and J-submodules in module theory.

Findings

Defined dual notions of r-, n-, and J-submodules

Established basic properties and relationships of these dual submodules

Extended the theoretical understanding of submodule structures in modules

Abstract

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduce and investigate the dual notions of r-submodules, n-submodules, and J-submodules of M.