Afrika Matematika

, Volume 29, Issue 3–4, pp 463–475 | Cite as

Semihypergroups associated with ternary relations



Davvaz and Leoreanu-Fotea (Commun Algebra 38(10):3621–3636, 2010) studied binary relations on ternary semihypergroups. A ternary relation or triadic relation is a relation in which the number of places in the relation is three. Now, in this paper, instead of binary relations we consider ternary relations and instead of ternary semihypergroups we consider ordinary semihypergroups. Then, we study ternary relations on semihypergroups. In particular, we discuss some properties of compatible ternary relations on them.


Semihypergroup Hypergroup Ternary relation 

Mathematics Subject Classification



  1. 1.
    Anvariyeh, S.M., Momeni, S.: \(n\)-ary hypergroups associated with \(n\)-ary relations. Bull. Korean Math. Soc. 50(2), 507–524 (2013)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Chvalina, J.: Commutative hypergroups in the sense of Marty and ordered sets. In: Proceedings of the Summer School on General Algebra and Ordered Sets Olomouc (Czech Republic), pp. 19–30 (1994)Google Scholar
  3. 3.
    Chvalina, J., Hošková-Mayerová, Š., Deghan Nezhad, A.: General actions of hyper-groups and some applications. An. Stiint. Univ. “Ovidius” Constanta Ser. Mat. 21(1), 59–82 (2013)MathSciNetGoogle Scholar
  4. 4.
    Chvalina, J., Hošková-Mayerová, Š.: On certain proximities and preorderings on the transposition hypergroups of linear first-order partial differential operators. An. Stiint. Univ. “Ovidius” Constanta Ser. Mat. 22(1), 85–103 (2014)MathSciNetMATHGoogle Scholar
  5. 5.
    Corsini, P.: Hypergraphs and hypergroups. Algebra Univers. 35, 548–555 (1996)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Corsini, P., Leoreanu, V.: Applications of Hyperstructures Theory. Advances in Mathematics. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  7. 7.
    Cristea, I., Ştefănescu, M.: Binary relations and reduced hypergroups. Discret. Math. 308, 3537–3544 (2008)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Cristea, I., Ştefănescu, M.: Hypergroups and \(n\)-ary relations. Eur. J. Comb. 32, 72–81 (2011)CrossRefMATHGoogle Scholar
  9. 9.
    Cristea, I.: Several aspects on the hypergroups associated with \(n\)-ary relations. An. St. Univ. Ovidius Constanta 17(3), 99–110 (2009)MathSciNetMATHGoogle Scholar
  10. 10.
    Cristea, I., Stefanescu, M., Angheluta, C.: About the fundamental relations defined on the hypergroupoids associated with binary relations. Eur. J. Comb. 32, 72–81 (2011)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Davvaz, B., Dehghan Nezhad, A., Benvidi, A.: Chain reactions as experimental examples of ternary algebraic hyperstructures. MATCH Commun. Math. Comput. Chem. 65(2), 491–499 (2011)MathSciNetGoogle Scholar
  12. 12.
    Davvaz, B., Dehghan Nezhad, A., Benvidi, A.: Chemical hyperalgebra: dismutation reactions. MATCH Commun. Math. Comput. Chem. 67, 55–63 (2012)MathSciNetGoogle Scholar
  13. 13.
    Davvaz, B., Dehghan Nezhad, A.: Dismutation reactions as experimental verifications of ternary algebraic hyperstructures. MATCH Commun. Math. Comput. Chem. 68, 551–559 (2012)MathSciNetGoogle Scholar
  14. 14.
    Davvaz, B., Karimian, M.: On the \(\gamma _n^*\)-complete hypergroups. Eur. J. Comb. 28, 86–93 (2007)CrossRefMATHGoogle Scholar
  15. 15.
    Davvaz, B., Leoreanu-Fotea, V.: Binary relations on ternary semihypergroups. Commun. Algebra 38(10), 3621–3636 (2010)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Davvaz, B., Dehghan Nezad, A., Heidari, M.M.: Inheritance examples of algebraic hyperstructures. Info. Sci. 224, 180–187 (2013)Google Scholar
  17. 17.
    Dehghan Nezhad, A., Moosavi Nejad, S.M., Nadjafikhah, M., Davvaz, B.: A physical example of algebraic hyperstructures: leptons. Indian J. Phys. 86(11), 1027–1032 (2012)CrossRefGoogle Scholar
  18. 18.
    Freni, D.: Strongly transitive geometric spaces: applications to hypergroups and semigroups theory. Commun. Algebra 32(8), 969–988 (2004)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Freni, D.: A new characterization of the derived hypergroup via strongly regular equivalences. Commun. Algebra 30(8), 3977–3989 (2002)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Freni, D.: Une note sur le coeur d’un hypergroupe et sur la cloture \(\beta ^*\) de \(\beta \). Mat. Pura e Appl. 8, 153–156 (1991)MATHGoogle Scholar
  21. 21.
    Ghadiri, M., Davvaz, B., Nekouian, R.: \(H_v\)-semigroup structure on \(F_2\)-offspring of a gene pool. Int. J. Biomath. 5(4), 1250011 (2012)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Koskas, M.: Groupoides, Demi-hypergroupes et hypergroupes. J. Math. Pure Appl. 49, 155–192 (1970)MathSciNetMATHGoogle Scholar
  23. 23.
    Leoreanu-Fotea, V., Davvaz, B.: \(n\)-hypergroups and binary relations. Eur. J. Comb. 29(5), 1207–1218 (2008)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Marty, F.: Sur une generalization de la notion de groupe, \(8^{iem}\) congres Math., pp. 45–49. Scandinaves, Stockholm (1934)Google Scholar
  25. 25.
    Nieminen, J.: Join space graphs. J. Geom. 33, 99–103 (1988)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Novak, V., Novotny, M.: Pseudodimension of relational structures. Czech. Math. J. 49(124), 547–560 (1999)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Rosenberg, I.G.: Hypergroups and join spaces determined by relations. Ital. J. Pure Appl. Math. 4, 93–101 (1998)MathSciNetMATHGoogle Scholar
  28. 28.
    Spartalis, S., Mamaloukas, C.: Hyperstructures and associated with binary relations. Comput. Math. Appl. 51(1), 41–50 (2006)MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Ştefănescu, M.: Some interpretations of hypergroups. Bull. Math. Soc. Sci. Math. Roum. 49(97)(1), 99–104 (2006)MathSciNetMATHGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsPayame Noor UniversityTehranIran
  2. 2.Department of MathematicsYazd UniversityYazdIran

Personalised recommendations