Weak Non-associative Structures of Groups with Applications

Main Article Content

Shah Nawaz
Muhammad Gulistan
Naveed Yaqoob
Seifedine Kadry

Abstract

Inspiring by the weak symmetry occurring in the Hv-left invertive structures, in this article we have introduce a new class of Hv-LA-groups which is a generalization of LA-hypergroups. We have investigated different types of homomorphisms of Hv-LA-groups. Moreover, we have constructed the HvLA-groups. At the end a useful application of weak symmetry related with Hv-left invertive structure has been presented using the chemical redox reaction.

Article Details

References

  1. M. A. Kazim and M. Naseeruddin, On almost semigroups, Aligarh Bull. Math., 2 (1972), 1-7.
  2. Q. Mushtaq and S. M. Yusuf, On LA-semigroups, Aligarh Bull. Math., 8 (1978), 65-70.
  3. P. Holgate, Groupoids satisfying a simple invertive law, Math. Stud., 61(1-4) (1992), 101-106.
  4. J. R. Cho, J. Jezek and T. Kepka, Paramedial groupoids, Czechoslovak Math. J., 49(2) (1999), 277-290.
  5. M. Akram, N. Yaqoob and M. Khan, On (m, n)-ideals in LA-semigroups, Appl. Math. Sci., 7(44) (2013), 2187-2191.
  6. M. Khan and N. Ahmad, Characterizations of left almost semigroups by their ideals, J. Adv. Res. Pure Math., 2(3) (2010), 61-73.
  7. P. V. Protic and N. Stevanovic, AG-test and some general properties of AbelGrassmann's groupoids, Pure Math. Appl., 6(4) (1995), 371-383.
  8. N. Stevanovic and P.V. Protic, Composition of Abel-Grassmann's 3-bands, Novi Sad J. Math., 34(2) (2004), 175-182.
  9. Q. Mushtaq and S.M. Yusuf, On locally associative LA-semigroups, J. Nat. Sci. Math., 19(1) (1979), 57-62.
  10. Q. Mushtaq and M. S. Kamran, Left almost group, Proc. Pak. Acad Sci., 33 (1996), 12
  11. F. Marty, Sur une generalization de la notion de groupe, 8iem Congres des Mathematicians Scandinaves Tenua Stockholm, (1934) 45-49.
  12. P. Corsini, Prolegomena of hypergroup theory, Aviani Editore, (1993).
  13. T. Vougiouklis, Hyperstructures and their representations, Hadronic Press,Palm Harbor, Flarida, USA, (1994).
  14. P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic, (2003).
  15. K. Hila and J. Dine, On hyperideals in left almost semihypergroups, ISRN Algebra, 2011 (2011), Article ID 953124.
  16. N. Yaqoob, P. Corsini and F. Yousafzai, On intra-regular left almost semihypergroups with pure left identity, J. Math., 2013 (2013), Article ID 510790.
  17. T. Vougiouklis, The fundamental relation in hyperrings. The general hyperfield, Algebraic Hyperstructures and Applications, Proceedings of the Fourth International Congress, (1991), 203-211.
  18. T. Vougiouklis, A new class of hyperstructures, Journal of Combinatorics, Inform. Syst. Sci., 20 (1995), 229-235.
  19. T. Vougiouklis, ∂-operations and Hv-fields, Acta Math. Sin. (Engl. Ser.), 24(7) (2008), 1067-1078.
  20. T. Vougiouklis, The h/v-structures, Algebraic Hyperstructures and Applications, Taru Publications, New Delhi, (2004), 115-123.
  21. S. Spartalis, On Hv-semigroups, Italian J. Pure Appl. Math., 11 (2002), 165-174.
  22. S. Spartalis, On the number of Hv-rings with P-hyperoperations, Discr. Math., 155 (1996), 225-231.
  23. S. Spartalis, On reversible Hv-group, Algebr. Hyperstruct. Appl., (1994) 163-170.
  24. S. Spartalis, Quoitients of P-Hv-rings, New Front. Hyperstruct., (1996) 167-176.
  25. S. Spartalis and T. Vougiouklis, The fundamental relations on Hv-rings, Riv. Mat. Pura Appl., 7 (1994), 7-20.
  26. M. Gulistan, N. Yaqoob and M. Shahzad, A Note On Hv-LA-semigroup U.P.B. Sci. Bull., Series A, 77 (3) (2015), 93-106
  27. B. Davvaz, Weak algebraic hyperstructures as a model for interpretation of chemical reactions, Iran. J. Math. Chem. 7 (2) (2016), 267-283.
  28. B. Davvaz, A. Dehghan Nezhad, A. Benvidi, Chemical hyperalgebra: Dismutation reactions, MATCH Commun. Math. Comput. Chem. 67 (2012), 55-63.
  29. B. Davvaz, A. D. Nezad and A. Benvidi, Chain reactions as experimental examples of ternary algebraic hyperstructures, MATCH Commun. Math. Comput. Chem. 65 (2) (2011), 491-499.