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On the topological structure of spectrum of intuitionistic L-fuzzy prime submodules

P. K. Sharma|Kanchan
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2021.04|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제21권 제2호|pp. 195-215|DOI 10.30948/afmi.2021.21.2.195

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참고문헌

키워드

Zariski topologyIntuitionistic $L$-fuzzy prime submodulesIntuitionistic $L$-fuzzy prime Spectrum$L$-top modules

초록

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. We topologize $IF_{L}Spec(M)$, the collection of all intuitionistic $L$-fuzzy prime submodules of $M$, analogous to that for $IFSpec(R)$, the spectrum of intuitionistic fuzzy prime ideals of $R$, and investigate the properties of this topological space. In particular, we will study the relationship between $IF_{L}Spec(M)$ and $IF_{L}Spec(R/Ann(M))$ and obtain some results. Also, we investigate the irreducible elements in this space.

Abstract

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. We topologize $IF_{L}Spec(M)$, the collection of all intuitionistic $L$-fuzzy prime submodules of $M$, analogous to that for $IFSpec(R)$, the spectrum of intuitionistic fuzzy prime ideals of $R$, and investigate the properties of this topological space. In particular, we will study the relationship between $IF_{L}Spec(M)$ and $IF_{L}Spec(R/Ann(M))$ and obtain some results. Also, we investigate the irreducible elements in this space.

참고문헌 (27)

  1. H. V. Kumbhojkar, "Spectrum of prime fuzzy ideals", Fuzzy Sets and Systems, 62, pp.101~109 (1994)
  2. C. P. Lu, "The Zariski topology on the Prime Spectrum of a Module", Houston J. Math, 25(3), pp.417~425 (1999)
  3. R. L. McCasland, "On the spectrum of a module over a commutative ring", Comm. Algebra, 25(1), pp.79~103 (1997)
  4. H. A. Toroghy, "On the prime spectrum of a module and Zariski topologies", Communications in Algebra, 38, pp.4461~4475 (2010)
  5. K. T. Atanassov, "Intuitionistic fuzzy sets", vii ITKR0s session (1983), Central Science and Technology Library of the Bulgarian Academy of Sci
  6. K. T. Atanassov, "Cybernetics and System Research 2", pp.539~540 (1984), Elsevier Sci. Publ
  7. K. T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20, pp.87~96 (1986)
  8. L. A. Zadeh, "Fuzzy sets", Information and control, 8, pp.338~353 (1965)
  9. J. Goguen, "L-fuzzy sets", Jour. Math. Anal. Appl, 18, pp.145~174 (1967)
  10. W. B. V. Kandasamy, "Smarandache Fuzzy Algebra" (2003), American Research Press
  11. J. N. Mordeson, "Fuzzy Commutative Algebra" (1998), World Scientific publishing Co. Pvt. Ltd
  12. B. Davvaz, "Intuitionistic fuzzy Hv-submodules", Inform. Sci, 176, pp.285~300 (2006)
  13. S. Rahman, "Some Aspects of Atanassov, s Intuitionistic Fuzzy Submodules", International Journal of Pure and Applied Mathematics, 77(3), pp.369~383 (2012)
  14. P. Isaac, "On intuitionistic fuzzy submodules of a modules", International Journal of Mathematical Sciences and Applications, 1(3), pp.1447~1454 (2011)
  15. D. K. Basnet, "Topics in intuitionistic fuzzy algebra" (2011), Lambert Academic Publishing
  16. P. K. Sharma, "(α, β)-cut of intuitionistic fuzzy modules", International Journal of Mathematical Sciences and Applications, 1(3), pp.1489~1492 (2011)
  17. P. K. Sharma, "On intuitionistic L-fuzzy prime submodules", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 16(1), pp.87~97 (2018), 기초자연과학연구소[DOI]
  18. P. K. Sharma, "On annihilator of intuitionistic fuzzy subsets of modules", Proceeding of Third International Conference on Fuzzy Logic Systems (Fuzzy-2017), pp.37~49 (2017), SIGEM, CSEA
  19. P. K. Sharma, Kanchan, "Simple and Semi-simple Intuitionistic L-fuzzy modules", ~
  20. I. Bakhadach, "Intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring", Notes on Intuitionistic Fuzzy Sets, 22(2), pp.59~63 (2016)
  21. 허걸, "Intuitionistic Fuzzy Ideals of a Ring", 순수 및 응용수학, 12(3), pp.193~209 (2005), 한국수학교육학회
  22. K. Meena, "Intuitionistic L-fuzzy Subrings", International Mathematical Forum, 6(52), pp.2561~2572 (2011)
  23. K. Meena, "Intuitionistic L-Fuzzy Rings", Global Journal of Science Frontier Research Mathematics and Decision Sciences, 12(14), pp.16~31 (2012)
  24. P. K. Sharma, "Residual quotient and annihilator of intuitionistic fuzzy sets of ring and module", International Journal of Computer Science and Information Technology(IJCSIT), 9(4), pp.1~15 (2017)
  25. P. K. Sharma, "Intuitionistic fuzzy prime spectrum of a ring", CiiT International Journal of Fuzzy Systems, 9(8), pp.167~175 (2017)
  26. Gareett Birkhoff, "Lattice Theory Vol. 25", American Mathematical Society Colloquium Publications, 25 (1969)
  27. Kanchan, "Intuitionistic L-fuzzy modules", Advances in Fuzzy Sets and Systems, 25(2), pp.123~142 (2020)

관련 논문AI추천

On intuitionistic L-fuzzy prime submodulesKanchan, P. K. Sharma기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2018 · 제16권 제1호On intuitionistic fuzzy multiplication modulesP. K. Sharma기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2022 · 제23권 제3호Topological dimension of pseudo-prime spectrum of modulesDawood Hassanzadeh-Lelekaami, Hajar Roshan-Shekalgourabi대한수학회 · 대한수학회논문집2017 · 제32권 제3호Intuitionistic fuzzification of essential submodule with respect to an arbitrary submoduleP. K. Sharma기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2020 · 제20권 제3호On Noetherian pseudo-prime spectrum of a topological le-moduleAnjan Kumar Bhuniya, Manas Kumbhakar대한수학회 · 대한수학회논문집2023 · 제38권 제1호On the Classical Zariski Topology Over Prime Spectrum of a ModuleMUSTAFA ALKAN, Seçil ÇEKEN장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제4호

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