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 AM  Vol.7 No.5 , March 2016
Group Action on Fuzzy Modules
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.
Cite this paper: Yamin, M. and Sharma, P. (2016) Group Action on Fuzzy Modules. Applied Mathematics, 7, 413-421. doi: 10.4236/am.2016.75038.
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