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

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.

arXiv commentI have divided the contents of this article into two articles and strengthened it. In addition, I changed the name of the articles