Abstract

Let R be a commutative ring with identity, and Y be a fuzzy module of an R- module M where M is a left untial module. In this paper we investigate a class of F. submodules called weakly essential fuzzy submodules that lie between essential fuzzy submodules and semi-essential fuzzy submodules. Also, we present the concept of weakly uniform fuzzy modules as a generalization of uniform fuzzy modules. This concept lies between Uniform fuzzy modules and semi-uniform fuzzy modules. Some basic properties, characteristics and examples of weakly essential fuzzy submodules and weakly uniform fuzzy modules are investigated, and some relationships among weakly essential fuzzy submodules, weakly uniform fuzzy modules and other related fuzzy submodules (fuzzy modules) are given.

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