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Title of paper: Exact sequence of intuitionistic fuzzy G-modules
Author(s):
Poonam Kumar Sharma
Post Graduate Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
pksharma@davjalandhar.com
Published in: "Notes on IFS", Volume 23, 2017, Number 5, pages 66—84
Download:  PDF (230 Kb  Kb, File info)
Abstract: The concept of intuitionistic fuzzy G-modules and their properties are defined and discussed by the author et al. in [16]. In this paper we develop the notion of exact sequence of intuitionistic fuzzy G-modules and study their properties.
Keywords: Intuitionistic fuzzy G-submodule, Quotient G-modules, Exact sequence.
AMS Classification: 03F55, 16D10, 08A72
References:
  1. Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) 87–96.
  2. Atanassov, K. T. (1994) New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61 137–142.
  3. Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag, Heidelberg.
  4. Basnet, D. K. (2011) Topics in intuitionistic fuzzy algebra, Lambert Academic Publishing,
  5. Biswas, R. (1989) Intuitionistic fuzzy subgroup, Mathematical Forum, X, 37–46.
  6. Bland, P. E. (2011) Rings and Their Modules, Walter de Gruyter Publishing.
  7. Curties, C. W., & Reiner, I. (1962) Representation Theory of finite groups and associated algebras, Interscience Publishers.
  8. Hur, K., Kang, H. W., & Song, H. K. (2003) Intuitionistic Fuzzy Subgroups and Subrings, Honam Math J. 25(1), 19–41.
  9. 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.
  10. Isaac, P. & Pearly, P. J. (2011) On Intuitionistic Fuzzy Submodules of a Module, Int. J. of Mathematical Sciences and Applications, 1(3), 1447–1454.
  11. Rahman, S., & Saikia, H. K. (2012) Some aspects of Atanassov0s intuitionistic fuzzy submodules, Int. J. Pure and Appl. Mathematics, 77(3), 369–383.
  12. Sharma, P. K. (2016) On intuitionistic fuzzy abelian subgroups - II, Advances in Fuzzy Sets and Systems, 21(1), 1–6.
  13. Sharma, P. K. (2015) Intuitionistic fuzzy representations of intuitionistic fuzzy groups, Asian Journal of Fuzzy and Applied Mathematics, 3(3), 81–94.
  14. Sharma, P. K. (2013) (α,β)-Cut of Intuitionistic fuzzy modules - II, International Journal of Mathematical Sciences and Applications, 3(1), 11–17.
  15. Sharma, P. K., & Kaur, G. (2016) Intuitionistic fuzzy superfluous submodule, Notes on Intuitionistic Fuzzy Sets, 22(3), 34–46.
  16. Sharma, P. K., & Kaur, T. (2015) Intuitionistic fuzzy G-modules, Notes on Intuitionistic Fuzzy Sets, 21(1), 6–23.
  17. Sharma, P. K., & Kaur, T. (2016) On intuitionistic fuzzy representation of intuitionistic fuzzy G-modules, Annals on Fuzzy Mathematics and Informatics, 11(4), 557–569.
  18. Sharma, P. K. (2016) Reducibility and Complete Reducibility of intuitionistic fuzzy G-modules, Annals of Fuzzy Mathematics and Informatics, 11(6), 885–898.
  19. Sharma, P. K. (2016) Isomorphism theorems for intuitionistic fuzzy submodules of G-modules, Notes on Intuitionistic Fuzzy Sets, 22(4), 80–88.
  20. Sharma, P. K. (2016) Semi simple intuitionistic fuzzy G-modules, International Journal of Pure and Applied Researches, 1(2), 101–108.
  21. Sharma, P. K. & Chopra, S. (2016). Projectivity of intuitionistic fuzzy G-modules, Advances in Fuzzy Sets and System, 21(3), 239–264.
  22. Sharma, P. K. & Chopra, S. (2016) Injectivity of intuitionistic fuzzy G-modules, Annals of Fuzzy Mathematics and Informatics, 12(6), 805–823.
  23. Sharma, P. K. (2016) Direct Sum of Intuitionistic Fuzzy Submodules of G-module, Asian Journal of Fuzzy and Applied Mathematics, 4(4), 36–46.
  24. Sharma, P. K. (2016) On Intuitionistic Fuzzy G-modules of GF(pn), Asian Journal of Fuzzy and Applied Mathematics, 4(4), 47–53.
  25. Zadeh, L.A. (1965) Fuzzy sets, Information and Control, 8, 338–353.
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