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Group Action on Fuzzy Modules
Faculty of Economics and Administration, King Abdulaziz University, Jeddah, Saudi Arabia
Department of Mathematics, D.A.V. College, Jalandhar City, India
- 1 Faculty of Economics and Administration, King Abdulaziz University, Jeddah, Saudi Arabia
- 2 Department of Mathematics, D.A.V. College, Jalandhar City, India
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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.
KeywordsFuzzy Submodule (FSM)Fuzzy Prime Submodule (FPSM)Fuzzy Semi Prime SubmoduleGroup Action (FSPSM)G-Invariant SubmoduleG-Module Homomorphism
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