Document Type : Research Paper

Authors

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

Main Subjects

###### ##### References

[1] I. Chon, Properties of fuzzy topological groups and semigroups, Kangweon-Kyungki Math. Jour, 8, (2000), 103–110.

[2] N.S. Gopalakrishnan, Commutative algebra, Oxonian Press Pvt, University of Poona,1984.

[3] C. Gunduz(Aras) and S. Bayramov, Inverse and direct system in category of fuzzy modules, Fuzzy Sets, Rough Sets and Multivalued Operations and Applications, 3, (2011), 11-25.

[4] K.H. Lee, On fuzzy quotient rings and chain conditions, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math, 7(1), (2000) 33-40.

[5] S.R. Lopez-Permouth and D.S. Malik, On Categories of Fuzzy Modules, Information Sciences, 52, (1990), 211-220.

[6] D.S. Malik, Fuzzy maximal, radical, and primary ideals of a ring, Information science, 53, (1991), 237-250.

[7] D.S. Malik and John.N. Mordeson, Fuzzy direct sums of fuzzy rings, Fuzzy Sets and Systems, 45, (1992), 83-91.

[8] J.N. Mordeson and D.S. Malik, Fuzzy Commutative Algebra, World Scientiﬁc, 1998.

[9] G.C. Muganda, Free fuzzy modules and their bases, Inform. Sci, 72, (1993), 65-82.

[10] V. Murali and B. Makamba, On Krull's intersection theorem of fuzzy ideals, International journal of mathematics and mathematical sciences, 4, (2003), 251-262.

[11] C.V. Negoita and D.A. Ralescu, Applications of Fuzzy Sets and System Analysis, Birkhauser, Basel, 1975.

[12] A. Rosenfeld, Fuzzy groups, J1. Math. Anal. Appl., 35, (1971), 512-517.

[13] L.A. Zadeh, Fuzzy sets, Inform. Control, 81, (1965), 338-353.

[14] M.M. Zahedi and A. Ameri, Fuzzy exact sequences in category of fuzzy modules, Jl. Fuzzy Math., 2(2), (1994), 409-424.