Fuzzy submodules

In this thesis the concept of module of classical algebra is analyzed within the context of the fuzzy algebra. Initially, the basic properties and theorems are given about the subject.Then fuzzy module is defined and the relation between the fuzzy module and the module in classical algebra is demonstrated. It has been noted that how a fuzzy module structure should be formed with examples. Following that, we noted that how the fuzzy submodules of quotient modules are combined. In this section, the expression of the concept of weak homomorphism and isomorphism with the fuzzy modules takes place. After the modules that are created by the fuzzy subset is demonstrated, free fuzzy modulesare introduced as a reflection of free modules. Given the residual quotients, primary fuzzy submodules are presented. As a result, this thesis is about relations between the concept of modules of classical algebra and the fuzzy modules. It is also a well-qualified thesis that poses a basic resource for whom may study in this field. Our following efforts will focus on what the reflection of other fields of the modules within the fuzzy algebra is and could be. Keywords: Fuzzy subgroup, Fuzzy rings, Fuzzy ideals, Fuzzy modules, Fuzzy submodules.