Partially Ordered Gamma Near-Rings

  • T. NagaiahEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


The notions of partially ordered Γ-near-ring(POGN), T-fuzzy ideal of POGN(TFIPOGN), T-fuzzy K-ideal of a POGN(TFKIPOGN), quotient POGN, and normal TFKIPOGN are introduced and investigated the basic properties. I also propose some necessary sufficient conditions on POGN under the T-norm.



The author is grateful to the referees for their careful reading and valuable suggestions which helped in improving this paper. I am also thankful to the editors for their valuable comments and suggestions.


  1. 1.
    Akram, M.: On T-Fuzzy Ideals in Near-rings, International Journal of Mathematics and Mathematical Sciences., 1–14 (2007).CrossRefGoogle Scholar
  2. 2.
    Anderson, David F., Badawi, A.: The total graph of a commutative ring, Journal of Algebra., 320, 2706–2719 (2008).MathSciNetCrossRefGoogle Scholar
  3. 3.
    Barnes, W. E.: On the Gamma-rings of Nobusawa, Pacific Journal of Maths., 18 , 411–422 (1966).CrossRefGoogle Scholar
  4. 4.
    Davvaz, B.: Fuzzy Ideals of Near-rings with interval valued membership functions, J. Sci.I.R.Iran., 12(2), 171–175 (2001).Google Scholar
  5. 5.
    Jun, Y. B., Hong, S. M and Kim, HS.: Fuzzy ideals in near-rings, Bulletin of the Korean Mathematical Society., 35(3), 455–464 (1998).Google Scholar
  6. 6.
    Jun, Y. B., Kim, K. H., Ozturk, M. A.: Fuzzy maximal ideals of Gamma near-rings, Turkish Journal of Mathematics., 25(4), 457–464 (2001).MathSciNetzbMATHGoogle Scholar
  7. 7.
    Jun, Y. B., Sapanci, M and Ozturk, M. A.: Fuzzy ideal in Gamma near-ring, Tr. J. Of mathematics., 22, 449–459 (1998).Google Scholar
  8. 8.
    Kim, S. D and kim, H. S.: On fuzzy ideal of near-rings, Bull Korean Math.Soc., 33(4), 593–601 (1996).Google Scholar
  9. 9.
    Meldrum, J. D. P.: Near-rings and their links with groups, Pitman London, (1985).Google Scholar
  10. 10.
    Muralikrishna Rao, M.: T-Fuzzy ideals in ordered Γ-semirings, Annals of fuzzy Mathematics and informatics., 13(2), 253–276 (2017).MathSciNetGoogle Scholar
  11. 11.
    Nagaiah, T., Vijay kumar, K., Iampan, A and Srinivas, T.: A study of fuzzy ideals in PO-Γ-Semigroups, Palestine journal of mathematics., 6(2), 591–597 (2017).Google Scholar
  12. 12.
    Nagaiah, T., Vijay Kumar, K., Narasimha Swamy, P and Srinivas, T.: A Study of fuzzy ideals in PO-Γ-Semigroups in terms of anti fuzzy ideals, Annals of fuzzy mathematics and informatics., 14(3), 225–236 (2017).Google Scholar
  13. 13.
    Nagaiah, T., Bhaskar, L.: Fuzzy ideals of partially ordered Gamma near-rings, International journal scientific and innavative mathematical research (IJSIMR), 5(8), 8–14 (2017).Google Scholar
  14. 14.
    Nagaiah, T.: Contribution to near-ring theory and fuzzy ideals in near-rings and semirings, Doctoral thesis, Kakatiya University (2012).Google Scholar
  15. 15.
    Nobusawa, N.: On a generalization of the ring theory, Osaka J.Math., 1, 81–89 (1964)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Pilz, G.: Near-rings, North-Holland mathematics studies, (1977).Google Scholar
  17. 17.
    Radhakrishna, A.: On lattice ordered near-rings and Nonassociative Rings, Doctoral thesis, Indian Istitute of Technology, (1975).Google Scholar
  18. 18.
    Rosenfeld, A., Fuzzy group, Journal of Mathematics., 35, 512–517 (1971).zbMATHGoogle Scholar
  19. 19.
    Satyanarayana, Bh.: Contribution to near-ring theory, Doctoral thesis, Nagarjuna University (1984).Google Scholar
  20. 20.
    Zadeh, L. A.: Fuzzy sets, Information and control., 8(3), 338–353 (1965).MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zhan. J.: On properties of fuzzy left h-ideals in hemirings with t-norms, International Journal of Mathematics and Mathematical Sciences., 19, 3127–3144 (2005).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsKakatiya UniveristyWarangalIndia

Personalised recommendations