Extension of Krull's intersection theorem for fuzzy module

Abstract

‎In this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules. It shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $mu$-adic completion.