As of August 2024, International Journal "Notes on Intuitionistic Fuzzy Sets" is being indexed in Scopus.
Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: September/October 2024.
Open Call for Papers: 22nd International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets • 18 October 2024 • Warsaw, Poland / online (hybrid mode).
Deadline for submissions: 1 October 2024.

Issue:Zariski topology on the spectrum of intuitionistic fuzzy classical primary submodules

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
(Redirected from Issue:Nifs/30/3/203-214)
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/30/3/203-214
Title of paper: Zariski topology on the spectrum of intuitionistic fuzzy classical primary submodules
Author(s):
Poonam Kumar Sharma
Post-Graduate Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
pksharma@davjalandhar.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 30 (2024), Number 3, pages 203–214
DOI: https://doi.org/10.7546/nifs.2024.30.3.203-214
Download:  PDF (242  Kb, File info)
Abstract: In this paper, we define and study the notion of intuitionistic fuzzy classical primary submodules over a unitary R-module M, where R is a commutative ring with unity. This is a generalisation of intuitionistic fuzzy primary ideals and intuitionistic fuzzy classical prime submodules. We further topologize the collection of all intuitionistic fuzzy submodules on an R-module M with a topology having the intuitionistic fuzzy primary Zariski topology on the intuitionistic fuzzy classical primary spectrum IFcpspec(M) as a subspace topology and investigate the properties of this topological space.
Keywords: Zariski topology, Classical primary submodule, Intuitionistic fuzzy classical primary submodule, Intuitionistic fuzzy classical primary spectrum, Intuitionistic fuzzy primary ideal.
AMS Classification: 54C50, 03F55, 16D10, 08A72, 16N80.
References:
  1. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets Theory and Applications. Studies on Fuzziness and Soft Computing, 35, Physica-Verlag, Heidelberg.
  2. Bakhadach, I., Melliani, S., Oukessou, M., & Chadli, S. L. (2016). Intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring. Notes on Intuitionistic Fuzzy Sets, 22(2), 59–63.
  3. Basnet, D. K. (2011). Topics in Intuitionistic Fuzzy Algebra. Lambert Academic Publishing, ISBN: 978-3-8443-9147-3.
  4. Baziar, M., & Behboodi, M. (2009). Classical primary submodules and decomposition theory of modules. Journal of Algebra and Its Applications, 8(3), 351–362.
  5. Behboodi, M., & Noori, M.J. (2009). Zariski-like topology on the classical prime spectrum of a modules. Bulletin of the Iranian Mathematical Society, 35(1), 255–271.
  6. Davvaz, B., Dudek, W. A., & Jun, Y. B. (2006). Intuitionistic fuzzy Hv-submodules. Information Sciences, 176, 285–300.
  7. Goswami, J., & Saikia, H. K. (2021). On the spectrum of weakly prime submodules. Thai Journal of Mathematics, 19(1), 51–58.
  8. Isaac, P., & John, P. P. (2011). On intuitionistic fuzzy submodules of a modules. International Journal of Mathematical Sciences and Applications, 1(3), 1447–1454.
  9. Lu, C. P. (1999). The Zariski topology on the prime spectrum of a module. Houston Journal of Mathematics, 25(3), 417–425.
  10. McCasland, R. L., Moore, M. E., & Smith, P. F. (1997). On the spectrum of a module over a commutative ring. Communications in Algebra, 25(1), 79–103.
  11. Sharma, P. K. (2022). On intuitionistic fuzzy primary ideal of a ring. Pan-American Journal of Mathematics, 1, 1–11.
  12. Sharma, P. K. (2023). Intuitionistic L-fuzzy classical prime and intuitionistic L-fuzzy 2-absorbing submodules. Notes on Intuitionistic Fuzzy Sets, 29(2), 99–113.
  13. Sharma, P. K., & Kanchan. (2020). On intuitionistic L-fuzzy primary and P -primary submodules. Malaya Journal of Matematik, 8(4), 1417–1426.
  14. Sharma, P. K., & Kanchan. (2020). Some topological properties of spectrum of intuitionistic fuzzy prime submodules. Malaya Journal of Matematik, 8(4), 1358–1362.
  15. Sharma, P. K., & Kaur, G. (2018). On intuitionistic fuzzy prime submodules. Notes on Intuitionistic Fuzzy Sets, 24(4), 97–112.
  16. Sharma, P. K., & Kaur, G. (2017). Residual quotient and annihilator of intuitionistic fuzzy sets of ring and module. International Journal of Computer Science and Information Technology, 9(4), 1–15.
  17. Sharma, P. K., & Kaur, G. (2017). Intuitionistic fuzzy prime spectrum of a ring. CiiT International Journal of Fuzzy Systems, 9(8), 167–175.
  18. Sharma, P. K., & Kaur, G. (2017). On annihilator of intuitionistic fuzzy subsets of modules. Proceeding of Third International Conference on Fuzzy Logic Systems (Fuzzy-2017) Chenai, India, 29-30 July, 2017 , pp. 37–49.
  19. Taherpour, A., Ghalandarzadeh, S., Rad, P. M., & Safari, P. (2022). On radical of intuitionistic fuzzy primary submodule. Hindawi Journal of Mathematics, Article ID 1332239.
  20. Toroghy, H. A., & Sarmazdeh, R. O. (2010). On the prime spectrum of a module and Zariski topologies. Communications in Algebra, 38, 4461–4475
Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.

Retrieved from "https://ifigenia.org/index.php?title=Issue:Zariski_topology_on_the_spectrum_of_intuitionistic_fuzzy_classical_primary_submodules&oldid=13582"