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A Note on Essential Soft Submodules
International Journal of Fuzzy Logic and Intelligent Systems 2019;19(1):10-17
Published online March 25, 2019
© 2019 Korean Institute of Intelligent Systems.

Bijan Davvaz1, Jing Ma2, and Chengxiz Sun3

1Department of Mathematics, Yazd University, Iran, 2Department of Mathematics, Jilin University, Changchun China, 3United Experimental School of AHSJU and Livon, Changchun, China
Correspondence to: Jing Ma (jma@jlu.edu.cn)
Received April 28, 2018; Revised December 17, 2018; Accepted March 18, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, we investigate the property of essential soft submodule and give an equivalent condition of essential soft submodule. Then the concept of the socle of a soft module is introduced, basic properties of such soft submodules are investigated, several equivalent definitions of the socle and the radical of a soft module are given respectively. Also, examples of these related soft submodules are given.
Keywords : Soft module, Essential soft submodule, Socle, Radical