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Submitted
June 13, 2017
Accepted
April 17, 2018
Published
May 18, 2018
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Abstract

The $\delta^n$-relation was introduced by Leoreanu-Fotea et. al.\cite{130}. In this article, we introduce the concept of$\delta^{n}$-heart of a hypergroup and we determine necessary andsufficient conditions for the relation $\delta^{n}$ to betransitive. Moreover, we determine a family $P_{\sigma}(H)$ ofsubsets of a hypergroup $H$ and we give sufficient conditionssuch that the geometric space $(H, P_{\sigma}(H))$ is stronglytransitive and the relation $\delta^n$ is transitive.

Keywords

Geometric spaces Hypergroup strongly regular relation

Article Details

Author Biographies

Saeed Mirvakili, Depratment of Mathematics, Payame Noor University, Tehran, Iran

Associate Professor of Mathematics, Payame Noor University, Tehran, Iran

Peyman Ghiasvand, Payame Noor University

Depratment of Mathematics, Payame Noor University, Tehran, Iran
How to Cite
Mirvakili, S., & Ghiasvand, P. (2018). Transitivity of The delta^n-Relation in Hypergroups. Journal of the Indonesian Mathematical Society, 24(2), 36–46. https://doi.org/10.22342/jims.24.2.524.36-46
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References

  1. bibitem{199} S. M. Anvariyeh, B. Davvaz, {it Stronglg transitive geometric spaces associated to hypermodules}, Journal of Algebra,
  2. (2009), 1340-1359.
  3. bibitem{2} P. Corsini, {it Prolegomena of hypergroup theory }, Aviani Editore, 1993.
  4. bibitem{3} P. Corsini and V. Leoreanu, {it Applications of hyperstructure theory},
  5. Advances in Mathematics, Kluwer Academic Publishers, 2003.
  6. bibitem{9} P. Corsini and V. Leoreanu, {it About the heart of a hypergroup}, Acta Univ. Carolin., 37 (1996) 17-28.
  7. bibitem{80} B. Davvaz, V. Leoreanu-Fotea, {it Hyperring Theory and
  8. Applications}, International Academic Press, USA, 2007.
  9. bibitem{88} B. Davvaz, M. Karimian , {it On the $gamma^{*}$-complete hypergroups}, European J. Combin., 28 (2007) 86-93.
  10. bibitem{10} D. Freni, {it A new characterization of the derived
  11. hypergroup via strongly regular equivalences}, Comm. Algebra,
  12. (8) (2002) 3977-3989.
  13. bibitem{100} D. Freni, {it Strongly transitive geometric spaces: Applications to hypergroups and semigroups theory},
  14. Comm. Algebra, 32(8) (2004) 969-988.
  15. bibitem{101} D. Freni, {it Une note sur le coeur $d^{,}$un hypergroupe et
  16. sur la cl^{o}ure $beta^{*}$ de $beta$ }, Riv. Mat. Pura Appl.,
  17. (8) (1970) 307-312.
  18. bibitem{190} M. Gutan, {it Properties of hyperproducts and the relation $beta$ in quasihpergroups},
  19. Ratio Mathmatica, 12 (1997) 19-34.
  20. bibitem{140} M. Koskas, {it Groupoides, demi-hypergroupes et hypergroupes},
  21. J. Math. Pures Appl., 49 (1970) 155-192.
  22. bibitem{120} M. Krasner, {it A class of hyperrings and hyperfields},
  23. Intern. J. Math. Math. Sci., 6(2) (1983) 307-312.
  24. bibitem{130} V. Leoreanu-Fotea, M. Jafarpour and S. Sh. Mousavi,
  25. {it The relation $delta^{n}$ and multisemi-direct hyperproducts
  26. of hypergroups}, Comm. Algebra, 40 (2012) 3597-3608.
  27. bibitem{121} F. Marty, {it Sur une generalization de la notion de groupe}, $8^{iem}$ congres Math. Scandinaves,
  28. Stockholm, (1934) 45-49.
  29. bibitem{123} S. Mirvakili, S. M. Anvariyeh and B. Davvaz,
  30. {it Transitivity of $Gamma$-relation on hyperfields}, Bull.
  31. Math. Soc. Sci. Math. Roumanie, Tome 51(99) No. 3 (2008) 233-243.
  32. bibitem{13} S. Mirvakili, S.M. Anvariyeh and B. Davvaz,
  33. {it On $alpha$-relation and transitivity conditions of
  34. $alpha$}, Comm. Algebra, 36 (2008) 1695–1703.
  35. bibitem{299} S. Mirvakili and B. Davvaz, {it Strongly transitive geometric spaces: applications to hyperrings,}
  36. Revista Uni'{o}n Matem'{a}tica Argentina, 53(1) (2012) 43-53.
  37. bibitem{17} T. Vougiouklis, {it Hyperstructures and Their Representations},
  38. Hadronice Press, Inc., Palm Harber, USA, (1994).
  39. bibitem{16} T. Vougiouklis, {it The fundamental relation in hyperrings. The
  40. general hyperfield}, Proc. Fourth Int. Congress on Algebraic
  41. Hyperstructures and Applications (AHA 1990), World Scientific,
  42. (1991) 203-211.