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

Faranak Farshadifar

Department of Mathematics, Farhangian University, Tehran, Iran

Email address: f.farshadifar@cfu.ac.ir

Doi : https://doi.org/10.47013/16.3.11

Cited by : Jordan J. Math & Stat., 16 (3) (2023), 551 - 562

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Received on: July 24, 2022;                                         Accepted on: Feb. 5, 2023

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

Keywords: n-submodule, J-submodule, co-n-submodule, and co-J-submodule.