Negoita C.V.has given the definition of fuzzy submodule,and that of some basic properties are studied.This paper not only gives the other definition of fuzzy submodule with irreducible nested set,but also discusses the equivalence of the two definitions.What's more,it gives the definition of fuzzy torsion submodule;especially fuzzy quotient module on the torsion submodule is defined.This paper yields the torsion element set is not empty under the fuzzy condition,which indicating that the conclusion of classical algebra that quotient module on the torsion submodule is torsion free module is no longer valid in fuzzy algebra.
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