FUZZY ESSENTIAL SUBMODULES WITH RESPECT TO AN ARBITRARY FUZZY SUBMODULE

FUZZY ESSENTIAL SUBMODULES WITH RESPECT TO AN ARBITRARY FUZZY SUBMODULE

S. Nimbhorkar, J. Khubchandani

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Abstract

In this paper, we extend the concepts of a fuzzy essential submodule and a fuzzy complement submodule to the concepts of fuzzy essential submodule with respect to an arbitrary fuzzy submodule and fuzzy complement submodule with respect to an arbitrary fuzzy submodule respectively. We give some characterizations and properties of such fuzzy submodules.

Keywords

Fuzzy submodule, Fuzzy essential submodule, Fuzzy complement submodule.