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Issue:Intuitionistic L-fuzzy classical prime and intuitionistic L-fuzzy 2-absorbing submodules

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Title of paper: Intuitionistic L-fuzzy classical prime and intuitionistic L-fuzzy 2-absorbing submodules
Author(s):
P. K. Sharma
Post-Graduate Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
pksharma@davjalandhar.com
Presented at: 26th International Conference on Intuitionistic Fuzzy Sets, Sofia, 26—27 June 2023
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 29 (2023), Number 2, pages 99–113
DOI: https://doi.org/10.7546/nifs.2023.29.2.99-113
Download:  PDF (253  Kb, File info)
Abstract: Let L be a complete lattice. We introduce and characterise intuitionistic L-fuzzy classical prime submodule and intuitionistic L-fuzzy 2-absorbing submodules of a unitary module M over a commutative ring R with identity. We compare both of these submodules with intuitionistic L-fuzzy prime submodules. It is proven that in the case of the multiplication module M, the two notions of intuitionistic L-fuzzy classical prime submodules and intuitionistic L-fuzzy prime submodules coincide. Many other related results concerning these notions are obtained.
Keywords: Intuitionistic L-fuzzy submodule, Intuitionistic L-fuzzy classical prime submodule, Intuitionistic L-fuzzy 2-absorbing submodule, Intuitionistic L-fuzzy prime (2-absorbing) ideal.
AMS Classification: 03F55, 08A72, 13C05, 13C13, 13C99.
References:
  1. Anderson, F. W., & Fuller, K. R. (1992). Rings and Categories of Modules (2nd edition). Springer Verlag.
  2. Atanassov, K., & Stoeva, S. (1984). Intuitionistic L-fuzzy sets. Cybernetics and System Research, 2, Elsevier Sci. Publ. Amsterdam, 539–540.
  3. Atani, S. E., & Farzalipour, F. (2007). On weakly prime submodules. Tamkang Journal of Mathematics, 38(3), 247–252.
  4. Azizi, A. (2008). On prime and weakly prime submodules. Vietnam Journal of Mathematics, 36(3), 315–325.
  5. Badawi, A. (2007). On 2-absorbing ideals of commutative rings. Bulletin of the Australian Mathematical Society, 75, 417–429.
  6. Bakhadach, I., Melliani, S., Oukessou, M. S., & Chadli, L. S. (2016). Intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring. Notes on Intuitionistic Fuzzy Sets, 22(2), 59–63.
  7. Behboodi, M., & Koohy, H. (2004). Weakly prime modules. Vietnam Journal of Mathematics, 32(2), 185–195.
  8. Behboodi, M., & Shojaee, S. H. (2010). On chains of classical prime submodules and dimension theory of modules. Bulletin of the Iranian Mathematical Society, 36, 149–166.
  9. Birkhoff, G. (1967). Lattice Theory. American Mathematical Society, Providence, Rhode Island.
  10. Darani, A. Y., & Soheilnia, F. (2011). 2-absorbing and weakly 2-absorbing submodules. Thai Journal of Mathematics, 9(3), 577–584.
  11. Dauns, J. (1978). Prime modules. Journal fur die reine und angewandte Mathematik, 298, 156–181.
  12. Deschrijver, G., & Kerre, E. E. (2003). On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems, 133 227–235.
  13. Goguen, J. (1967). L-fuzzy sets. Journal of Mathematical Analysis and Applications, 18, 145–174.
  14. Jamali, M., & Nezhad, R. J. (2022). On classical weakly prime submodules. Facta Universitatis, Series: Mathematics and Informatics, 37(1), 17–30.
  15. Kanchan, Sharma, P. K., & Pathania, D. S. (2020). Intuitionistic L-fuzzy submodules. Advances in Fuzzy Sets and Systems, 25(2), 123–142.
  16. Kasch, F. (1982). Modules and Rings. Academic Press, London.
  17. Meena, K., & Thomas, K. V. (2011). Intuitionistic L-fuzzy subrings. International Mathematics Forum 6(52), 2561–2572.
  18. Palaniappan, N., Naganathan, S., & Arjunan, K. (2009). A study on Intuitionistic L-fuzzy Subgroups. Applied Mathematics Sciences, 3(53), 2619–2624.
  19. Sharma, P. K. (2022). On intuitionistic fuzzy multiplication modules. Annals of Fuzzy Mathematics and Informatics, 23(3), 295–309.
  20. Sharma, P. K. (2022). On intuitionistic fuzzy primary ideal of a ring. Pan-American Journal of Mathematics, 1, 1–11.
  21. Sharma, P. K., & Kanchan. (2018). On intuitionistic L-fuzzy prime submodules. Annals of Fuzzy Mathematics and Informatics, 16(1), 87–97.
  22. Sharma, P. K., & Kanchan. (2020). On intuitionistic L-fuzzy primary and P-primary submodules. Malaya Journal of Matematik, 8(4), 1417–1426.
  23. Sharma, P. K., & Kanchan. (2021). On the topological structure of spectrum of intuitionistic L-fuzzy prime submodules. Annals of Fuzzy Mathematics and Informatics, 21(2), 195–215.
  24. Wang, G. J., & He, Y. Y. (2000). Intuitionistic fuzzy sets and L-fuzzy sets. Fuzzy Sets and Systems, 110, 271–274.
  25. Yavuz, S., Onar, S., Sonmez, D., & Ersoy, B. A. (2017). Intuitionistic fuzzy 2-absorbing primary ideals of commutative rings. Journal of Hyperstructures, 6, 56–71.
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