Extension of Krull's intersection theorem for fuzzy module

Authors

Ali Reza Sedighi Department of Mathematics, Faculty of mathematics and statistics, University of Birjand, Birjand, Iran.

Mohammad Hossein Hosseini Department of Mathematics, Faculty mathematics and statistics, University of Birjand, Birjand, Iran.

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.

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