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n-ARY HYPERGROUPS ASSOCIATED WITH n-ARY RELATIONS

  • Anvariyeh, Seid Mohammad (Department of Mathematics Yazd University) ;
  • Momeni, Somayyeh (Department of Mathematics Yazd University)
  • Received : 2011.10.26
  • Published : 2013.03.31

Abstract

The notion of $n$-ary algebraic hyperstructures is a generalization of ordinary algebraic hyperstructures. In this paper, we associate an n-ary hypergroupoid (H, $f$) with an ($n+1$)-ary relation ${\rho}_{n+1}$ defined on a non-empty set H. Then, we obtain some basic results in this respect. In particular, we investigate when it is an $n$-ary $H_v$-group, an $n$-ary hypergroup or a join $n$-ary space.

Keywords

hypergroup;binary relation;n-ary hypergroup;n-ary $H_v$-group;join n-ary space

References

  1. P. Corsini, Binary relations and hypergroupoids, Ital. J. Pure Appl. Math. 7 (2000), 11-18.
  2. P. Corsini and V. Leoreanu, Hypergroups and binary relations, Algebra Universalis 43 (2000), no. 4, 321-330. https://doi.org/10.1007/s000120050162
  3. I. Cristea and M. Stefanescu, Hypergroups and n-ary relations, European J. Combin. 31 (2010), no. 3, 780-789. https://doi.org/10.1016/j.ejc.2009.07.005
  4. B. Davvaz, W. A. Dudek, and T. Vougiouklis, A generalization of n-ary algebraic systems, Comm. Algebra 37 (2009), no. 4, 1248-1263. https://doi.org/10.1080/00927870802466835
  5. B. Davvaz and V. Leoreanu-Fotea, Binary relations for ternary semihypergroups, Comm. Algebra 38 (2010), no. 10, 3621-3636. https://doi.org/10.1080/00927870903200935
  6. B. Davvaz and T. Vougiouklis, n-ary hypergroups, Iran. J. Sci. Technol. Trans. A Sci. 30 (2006), no. 2, 165-174.
  7. M. De Salvo and J. Lo Faro, A new class of hypergroupoids associated to binary relations, J. Mult.-Valued Logic Soft Comput. 9 (2003), no. 4, 361-375.
  8. M. De Salvo and J. Lo Faro, Hypergroups and binary relations, Mult.-Valued Log. 8 (2002), no. 5-6, 645-657.
  9. D. Freni, A new characterization of the derived hypergroup via strongly regular equivalences, Comm. Algebra 30 (2002), no. 8, 3977-3989. https://doi.org/10.1081/AGB-120005830
  10. V. Leoreanu-Fotea and B. Davvaz, n-ary hypergroups and binary relations, European J. Combin. 29 (2008), no. 5, 1207-1218. https://doi.org/10.1016/j.ejc.2007.06.025
  11. V. Leoreanu-Fotea and B. Davvaz, Join n-spaces and lattices, J. Mult.-Valued Logic Soft Comput. 15 (2009), no. 5-6, 421-432.
  12. V. Leoreanu-Fotea and B. Davvaz, Roughness in n-ary hypergroups, Information Sciences 178 (2008), no. 21, 4114-4124. https://doi.org/10.1016/j.ins.2008.06.019
  13. V. Leoreanu and L. Leoreanu, Hyperstructures and binary relations, Sci. Ann. Univ. Agric. Sci. Vet. Med. 45 (2002), 69-72.
  14. F. Marty, Sur une generalization de la notion de group, 8th Congress Math Scandenaves, Stockholm, (1934), 45-49.
  15. S. Rasouli and B. Davvaz, Homomorphisms, ideals and binary relations on hyper-MV algebras, J. Mult.-Valued Logic Soft Comput. 17 (2011), no. 1, 47-68.
  16. I. G. Rosenberg, Hypergroups and Join spaces determined by relations, Ital. J. Pure Appl. Math. 4 (1998), 93-101.
  17. S. Spartalis, Hypergroupoids obtained from groupoids with binary relations, Ital. J. Pure Appl. Math. 16 (2004), 201-210.
  18. S. Spartalis and C. Mamaloukas, Hyperstructures associated with binary relations, Comput. Math. Appl. 51 (2006), no. 1, 41-50. https://doi.org/10.1016/j.camwa.2005.07.011
  19. T. Vougiouklis, Fundamental relations in hyperstructures, Bull. Greek Math. Soc. 42 (1999), 113-118.
  20. T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press Inc., Florida, 1994.
  21. T. Vougiouklis, A new class of hyperstructures, J. Combin. Inform. System Sci. 20 (1995), no. 1-4, 229-235.

Cited by

  1. n–ary hyperstructures constructed from binary quasi–ordered semigroups vol.22, pp.3, 2014, https://doi.org/10.2478/auom-2014-0056
  2. Semihypergroups associated with ternary relations vol.29, pp.3-4, 2018, https://doi.org/10.1007/s13370-018-0554-8