Abstract
In this paper, we introduce the notion of essential extensions of fuzzy modules. We use these concepts to introduce the notion of injective hulls of fuzzy modules. It is known that every [Formula: see text]-module has an injective hull, where [Formula: see text] is a ring. We show that these corresponding results do not hold for fuzzy [Formula: see text]-modules, i.e. there exists a fuzzy [Formula: see text]-module that does not have an injective hull. Sufficient conditions are given for a fuzzy [Formula: see text]-module to have an injective hull.
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