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has been cited by the following article:

• TITLE: Group Action on Fuzzy Modules

  AUTHORS: Mohammad Yamin, Poonam Kumar Sharma

  KEYWORDS: Fuzzy Submodule (FSM), Fuzzy Prime Submodule (FPSM), Fuzzy Semi Prime Submodule, Group Action (FSPSM), G-Invariant Submodule, G-Module Homomorphism

  JOURNAL NAME: Applied Mathematics, Vol.7 No.5, March 18, 2016

  ABSTRACT: In this article, we introduce the notion of fuzzy G-module by defining the group action of G on a fuzzy set of a Z-module M. We establish the cases in which fuzzy submodules also become fuzzy G-submodules. Notions of a fuzzy prime submodule, fuzzy prime G-submodule, fuzzy semi prime submodule, fuzzy G-semi prime submodule, G-invariant fuzzy submodule and G-invariant fuzzy prime submodule of M are introduced and their properties are described. The homomorphic image and pre-image of fuzzy G-submodules, G-invariant fuzzy submodules and G-invariant fuzzy prime submodules of M are also established.