Document Type : Research Paper
Authors
- Ali Reza Sedighi ^{} ^{1}
- Mohammad Hossein Hosseini ^{2}
^{1} Department of Mathematics, Faculty of mathematics and statistics, University of Birjand, Birjand, Iran.
^{2} 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.
Keywords
- $mu$-Fuzzy filtered module
- Fuzzy inverse system
- Fuzzy topological group
- Krull's intersection theorem
Main Subjects