The Dual of the Notions n-Submodules and J-Submodules

Abstract

Let R be a commutative ring with identity and M be an R-module. A proper submodule N of M is called an n-submodule if for a ∈ R, m ∈ M, am ∈ N with a ∈ Ann_R(M), implies m ∈ N. A proper submodule N of M is called a J-submodule of M if for a ∈ R and m ∈ M, whenever am ∈ N and a ∈ (J(R)M : M), then m ∈ N. The aim of this paper is to introduce and investigate the dual notions of n-submodules and J-submodules of M.

Key words and phrases. n-submodule, J-submodule, co-n-submodule, and co-J-submodule.

2010 Mathematics Subject Classification. 13C13, 13C99