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.