Author(s)

Mohammad Yamin¹, Poonam Kumar Sharma^2*

¹Faculty of Economics and Administration, King Abdulaziz University, Jeddah, Saudi Arabia.
²Department of Mathematics, D.A.V. College, Jalandhar City, India.

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.

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

Yamin, M. and Sharma, P. (2016) Group Action on Fuzzy Modules. Applied Mathematics, 7, 413-421. doi: 10.4236/am.2016.75038.