Issue:Intuitionistic fuzzy superfluous submodule

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Title of paper: Intuitionistic fuzzy superfluous submodule Author(s): Poonam Kumar Sharma Post Graduate, Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India pksharma@davjalandhar.com Gagandeep Kaur Research scholar, I. K. Gujral Punjab Technical University, Jalandhar, Punjab, India talktogagandeep@gmail.com Presented at: 20th International Conference on Intuitionistic Fuzzy Sets, 2–3 September 2016, Sofia, Bulgaria Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 22, 2016, Number 3, pages 34—46 Download:  PDF (132  Kb, File info) Abstract: In this paper, we introduce the notion of intuitionistic fuzzy superfluous (or small) submodule of a module and study some of their properties. We establish the condition of an intuitionistic fuzzy submodule to be an intuitionistic fuzzy superfluous submodule. A relationship between superfluous submodule and the intuitionistic fuzzy superfluous submodule is derived. We also study the nature of intuitionistic fuzzy superfluous submodules under intuitionistic fuzzy direct sum. A relation regarding intuitionistic fuzzy superfluous submodule and intuitionistic fuzzy quotient module is established. It is shown that the well-known relation between the Jacobson radical and the superfluous submodules does not hold in case of intuitionistic fuzzy superfluous submodules. Keywords: Intuitionistic fuzzy superfluous submodules, Intuitionistic fuzzy indecomposable modules, Intuitionistic fuzzy direct sum, Intuitionistic fuzzy radical. AMS Classification: 03F55, 16D10. References: Anderson, F. W. & Fuller K. R. (1992) Rings and Categories of Modules, Second edition, Springer Verlag. Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96. Atanassov, K. T. (1994) New operation defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142. Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications, Series Studies on Fuzziness and Soft Computing, Vol. 35, Springer Physica-Verlag, Heidelberg. Basnet, D. K., Sarma, N. K., & Singh, L. B. (2010) Fuzzy Superfluous Submodule, Proceedings of the 6th IMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010), 3–4 November, 2010, Kualalumpur, Malaysia., 330–335. Basnet, D. K. (2011) Topics in Intuitionistic Fuzzy Algebra, Lambert Academic Publishing, Germany. Biswas, R. (1989) Intuitionistic fuzzy subgroup, Mathematical Forum, X, 37–46. Bland Paul, E. (2012) Rings and Their Modules, Deutsche Nationalbibliothek, Germany. Goodearl, K. R. (1976) Ring Theory, Marcel Dekker INC, New York and Basel. Hur, K., Kang, H. W. & Song, H. K. (2003) Intuitionistic Fuzzy Subgroups and Subrings, Honam Math J., 25(1), 19–41. Hur, K., Jang, S. Y. & Kang, H. W. (2005) Intuitionistic Fuzzy Ideals of a Ring, Journal of the Korea Society of Mathematical Education, Series B, 12(3), 193–209. Isaac, P., & John, P. P. (2011) On Intuitionistic Fuzzy Submodules of a Module, Int. J. of Mathematical Sciences and Applications, 1(3), 1447–1454. John, P. P. & Isaac, P. (2012) IFSM’s of an R-Module – A Study, International Mathematical Forum, 19(7), 935–943. Negoita, C. V. & Ralescu, D. A. (1975) Applications of Fuzzy Sets and Systems Analysis, Birkhauser, Basel. Rahman, S. & Saikia, H. K. (2012) Some aspects of Atanassov’s intuitionistic fuzzy submodules, Int. J. Pure and Appl. Mathematics, 77(3), 369–383. Rosenfeld, A. (1971) Fuzzy group, J. Math. Anal. and Appl., 35, 512–517. Sharma, P. K. & Kaur, T. (2015) Intuitionistic fuzzy G-modules, Notes on Intuitionistic Fuzzy Sets, 21(1), 6–23. Sharma, P. K. (2013) (α,β)-Cut of intuitionistic fuzzy modules–II, Int. J. of Mathematical Sciences and Applications, 3(1), 11–17. Sharma, P. K. (2011) (α,β)-Cut of intuitionistic fuzzy modules Int. J. of Mathematical Sciences and Applications, 3(1), 1489–1492. Sharma, P. K. Reducibility and Complete Reducibility of intuitionistic fuzzy G-modules, Annals of Fuzzy Mathematics and Informatics (accepted). Zadeh, L. A. (1965) Fuzzy sets, Inform. Control., 8, 338–353. Citations: Issue:Exact sequence of intuitionistic fuzzy G-modules ‎ (← links) The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.