On Left Almost Semihyperrings

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Shah Nawaz, Inayatur Rehman, Muhammad Gulistan

Abstract

The purpose of this article is to introduce the notion of left almost semihyperrings which is a generalization of left almost semirings. We investigate the basic properties of left almost semihyperrings. By using the concept of hyperideal and regular relations we prove some useful results on it.

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References

  1. M. Azhar, M. Gulistan, N. Yaqoob and S. Kadry, On fuzzy ordered LA-semihypergroups, Int. J. Anal. Appl., 16(2) (2018) 276-289.
  2. J. R. Cho, J. Jezek and T. Kepka, Paramedial groupoids, Czechoslovak Math. J., 49(2) (1999) 277-290.
  3. P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, (1993).
  4. P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Kluwer Academic, (2003).
  5. M. Gulistan, N. Yaqoob and M. Shahzad, A note on H v -LA-semigroups, UPB Sci. Bull., Ser. A, 77(3) (2015) 93-106.
  6. M. Gulistan, M. Khan, N. Yaqoob and M. Shahzad, Structural properties of cubic sets in regular LA-semihypergroups, Fuzzy Inf. Eng., 9 (2017) 93-116.
  7. K. Hila and J. Dine, On hyperideals in left almost semihypergroups, ISRN Algebra, Article ID 953124 (2011) 8 pages.
  8. P. Holgate, Groupoids satisfying a simple invertive law, Math. Stud., 61(1-4) (1992) 101-106.
  9. M. Iqbal, and I. Ahmad, On further study of CA-AG-groupoids, Proc. Pakistan Acad. Sci., 53(3) (2016) 325-337.
  10. M.A. Kazim and M. Naseeruddin, On almost semigroups, Aligarh Bull. Math., 2 (1972) 1-7.
  11. R. Kellil, On inverses of left almost semirings and strong left almost semirings, J. Math. Sci., Adv. Appl., 26 (2014) 29-39.
  12. M. Khan, M. Gulistan, N. Yaqoob and F. Hussain, General cubic hyperideals of LA-semihypergroups, Afrika Mat., 27(3-4) (2016) 731-751.
  13. F. Marty, Sur une generalization de la notion de groupe, 8 im 5 z Congres Mathematicians Scandinaves Tenua Stockholm, (1934) 45-49.
  14. Q. Mushtaq and S.M. Yusuf, On LA-semigroups, Aligarh Bull. Math., 8 (1978) 65-70.
  15. Q. Mushtaq and S. M. Yousaf, On locally associative LA-semigroups, J. Nat. Sci. Math., 19 (1979), 57-62.
  16. Q. Mushtaq and M. S. Kamran: On left almost groups, Proc. Pakistan Acad. Sci., 331 (1996) 53-55.
  17. I. Rehman, N. Yaqoob and S. Nawaz, Hyperideals and hypersystems in LA-hyperrings, Songklanakarin J. Sci. Techn., 39(5) (2017) 651-657.
  18. M. Shah and T. Shah, Some basic properties of LA-ring, Int. Math. Forum, 6(44) (2011) 2195-2199.
  19. T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press, Palm Harbor, Flarida, USA, (1994).
  20. N. Yaqoob, P. Corsini and F. Yousafzai, On Intra-regular left almost semihypergroups with pure left identity, J. Math., 2013 (2013) Article ID 510790, 10 pages.
  21. N. Yaqoob and M. Gulistan, Partially ordered left almost semihypergroups, J. Egyptian Math. Soc., 23 (2015) 231-235.
  22. N. Yaqoob, I. Cristea, M. Gulistan and S. Nawaz, Left almost polygroups, Italian J. Pure Appl. Math., 39 (2018) 465-474.
  23. N. Yaqoob, M. Gulistan, V. Leoreanu-Fotea and K. Hila, Cubic hyperideals in LA-semihypergroups, J. Intell. Fuzzy Syst., 34(4) (2018) 2707-2721.
  24. N. Yaqoob, Applications of rough sets to Γ-hyperideals in left almost Γ-semihypergroups, Neural Comput. Appl., 21(1) (2012) 267-273.
  25. S. M. Yusuf, On Left Almost Ring, Proc. of 7th International Pure Math. Conference, Islamabad, (2006).
  26. J. Zhan, N. Yaqoob and M. Khan, Roughness in non-associative po-semihyprgroups based on pseudohyperorder relations, J. Multiple-Valued Logic Soft Comput., 28(2-3) (2017) 153-177.