Title: Direct Product of Finite Fuzzy Normal Subrings Over Non-Associative Rings
Author(s): Nasreen Kausar, Muhammad Azam Waqar
Pages: 752-770
Cite as:
Nasreen Kausar, Muhammad Azam Waqar, Direct Product of Finite Fuzzy Normal Subrings Over Non-Associative Rings, Int. J. Anal. Appl., 17 (5) (2019), 752-770.

Abstract


In this paper, we define the concept of direct product of finite fuzzy normal subrings over nonassociative and non-commutative rings (LA-ring) and investigate the some fundamental properties of direct product of fuzzy normal subrings.

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References


  1. R. J. Cho, J. Jezek and T. Kepka, Paramedial groupoids, Czechoslovak Math. J., 49 (1999) 277-290. Google Scholar

  2. K. A. Dib, N. Galhum and A. A. M. Hassan, Fuzzy rings and fuzzy ideals, Fuzzy Math., 4 (1996) 245-261. Google Scholar

  3. V. N. Dixit, R. Kumar and N. Ajmal, Fuzzy ideals and fuzzy prime ideals of a ring, Fuzzy Set Syst., 44 (1991) 127-138. Google Scholar

  4. K. C. Gupta and M. K. Kantroo, The intrinsic product of fuzzy subsets of a ring, Fuzzy Set Syst., 57 (1993) 103-110. Google Scholar

  5. J. Jezek and T. Kepka, Medial groupoids, Rozpravy CSAV Rada Mat. a Prir. Ved., 93/2, 1983, 93 pp. Google Scholar

  6. M. S. Kamran, Conditions for LA-semigroups to resemble associative structures, Ph.D. Thesis, Quaid-i-Azam University, Islamabad, 1993. Google Scholar

  7. N. Kausar, M. Waqar, Characterizations of non-associative rings by their intuitionistic fuzzy bi-ideals, Eur. J. Pure Appl. Math. 12 (2019), 226-250. Google Scholar

  8. N. Kausar, Characterizations of non-associative ordered semigroups by the properties of their fuzzy ideals with thresholds (α, β], Prikl. Diskr. Mat. 43 (2019), 37-59. Google Scholar

  9. N. Kausar, Direct product of finite intuitionistic fuzzy normal subrings over non-associative rings, Eur. J. Pure Appl. Math., 12 (2019), 622-648. Google Scholar

  10. M. A. Kazim and M. Naseeruddin, On almost semigroups, Alig. Bull. Math., 2 (1972), 1-7. Google Scholar

  11. N. Kausar, B. Islam, M. Javaid, S, Amjad, U. Ijaz, Characterizations of non-associative rings by the properties of their fuzzy ideals, J. Taibah Univ. Sci. 13 (2019), 820-833. Google Scholar

  12. N. Kausar, B. Islam, S. Amjad, M. Waqar, Intuitionistics fuzzy ideals with thresholds(,] in LA-rings, Eur. J. Pure Appli. Math. 12 (2019) 906-943. Google Scholar

  13. N. Kuroki, Regular fuzzy duo rings, Inform. Sci., 94 (1996), 119-139. Google Scholar

  14. W. J. Liu, Fuzzy invariant subgroups and ideals, Fuzzy Sets Syst., 8 (1982), 133-139. Google Scholar

  15. T. K. Mukherjee and M. K. Sen, On fuzzy ideals of a ring 1, Fuzzy Sets Syst., 21 (1987), 99-104. Google Scholar

  16. T. K. Mukherjee and M. K. Sen, Prime fuzzy ideals in rings, Fuzzy Sets Syst., 32 (1989), 337-341. Google Scholar

  17. M. T. A. Osman, On the direct product of fuzzy subgroups, Fuzzy Sets Syst., 12 (1984), 87-91. Google Scholar

  18. M. T. A. Osman, On some product of fuzzy subgroups, Fuzzy Sets Syst., 24 (1987), 79-86. Google Scholar

  19. P. V. Protic and N. Stevanovic, AG-test and some general properties of Abel-Grassmann’s groupoids, Pure Math. Appl., 6 (1995) 371-383. Google Scholar

  20. A. K. Ray, Product of fuzzy subgroups, Fuzzy Sets Syst., 105 (1999), 181-183. Google Scholar

  21. T. Shah, N. Kausar and I. Rehman, Intuitionistic fuzzy normal subrings over a non-associative ring, An. St. Univ. Ovidius Constanta, 1 (2012) 369-386. Google Scholar

  22. T. Shah, N. Kausar, Characterizations of non-associative ordered semigroups by their fuzzy bi-ideals, Theor. Comput. Sci. 529 (2014), 96-110. Google Scholar

  23. T. Shah and I. Rehman, On LA-rings of finitely non-zero functions, Int. J. Contemp. Math. Sci., 5 (2010) 209-222. Google Scholar

  24. H. Sherwood, Product of fuzzy subgroups, Fuzzy Sets Syst., 11 (1983) 65-77. Google Scholar

  25. U. M. Swamy and K. L. N. Swamy, Fuzzy prime ideals of rings, J. Math. Anal. Appl., 134 (1988) 94-103. Google Scholar

  26. L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965) 338-353. Google Scholar

  27. S. A. Zaid, On normal fuzzy subgroups, J. Fac. Educ. Ain Shams Univ. Cairo, 13 (1988), 115-125. Google Scholar