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Journal of Mathematics
Volume 2013, Article ID 915250, 7 pages
http://dx.doi.org/10.1155/2013/915250
Research Article

-Semihypergroups and Regular Relations

1Department of Mathematics, Payame Noor University, Tehran, Iran
2Department of Mathematics, Yazd University, Yazd, Iran

Received 30 October 2012; Accepted 29 December 2012

Academic Editor: Feng Feng

Copyright © 2013 S. Mirvakili et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Marty, “Sur une generalization de la notion de groupe,” in Proceedings of the 8th Congress des Mathematiciens Scandinaves, pp. 45–49, Stockholm, Sweden, 1934.
  2. P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, vol. 5 of Advances in Mathematics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003. View at MathSciNet
  3. P. Bonansinga and P. Corsini, “On semihypergroup and hypergroup homomorphisms,” Unione Matematica Italiana. Bollettino. B. Serie VI, vol. 1, no. 2, pp. 717–727, 1982 (Italian). View at Google Scholar · View at MathSciNet
  4. P. Corsini, “Sur les semi-hypergroupes,” Atti della Società Peloritana di Scienze Fisiche, Matematiche e Naturali, vol. 26, pp. 363–372, 1980 (French). View at Google Scholar · View at Zentralblatt MATH
  5. B. Davvaz, “Some results on congruences on semihypergroups,” Bulletin of the Malaysian Mathematical Sciences Society. Second Series, vol. 23, no. 1, pp. 53–58, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. B. Davvaz and N. S. Poursalavati, “Semihypergroups and S-hypersystems,” Pure Mathematics and Applications, vol. 11, pp. 43–49, 2000. View at Google Scholar
  7. D. Fasino and D. Freni, “Existence of proper semihypergroups of type U on the right,” Discrete Mathematics, vol. 307, no. 22, pp. 2826–2836, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. Guţan, “Simplifiable semihypergroups,” in Algebraic Hyperstructures and Applications (Xánthi, 1990), pp. 103–111, World Scientific Publishing, Teaneck, NJ, USA, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. Hasankhani, “Ideals in a semihypergroup and Green's relations,” Ratio Mathematica, no. 13, pp. 29–36, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. V. Leoreanu, “About the simplifiable cyclic semihypergroups,” Italian Journal of Pure and Applied Mathematics, no. 7, pp. 69–76, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. S. V. Onipchuk, “Regular semihypergroups,” Matematicheskiĭ Sbornik, vol. 183, no. 6, pp. 43–54, 1992 (Russian), translation in Russian Academy of Sciences. Sbornik Mathematics, vol. 76, pp. 155–164, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. K. Sen and N. K. Saha, “On Γ-semigroup. I,” Bulletin of the Calcutta Mathematical Society, vol. 78, no. 3, pp. 180–186, 1986. View at Google Scholar · View at MathSciNet
  13. S. Chattopadhyay, “Right inverse Γ-semigroup,” Bulletin of the Calcutta Mathematical Society, vol. 93, no. 6, pp. 435–442, 2001. View at Google Scholar · View at MathSciNet
  14. S. Chattopadhyay, “Right orthodox Γ-semigroup,” Southeast Asian Bulletin of Mathematics, vol. 29, no. 1, pp. 23–30, 2005. View at Google Scholar · View at MathSciNet
  15. K. Hila, “On some classes of le-Γ-semigroups,” Algebras, Groups and Geometries, vol. 24, pp. 485–495, 2007. View at Google Scholar
  16. N. K. Saha, “On Γ-semigroup. II,” Bulletin of the Calcutta Mathematical Society, vol. 79, no. 6, pp. 331–335, 1987. View at Google Scholar · View at MathSciNet
  17. M. K. Sen and S. Chattopadhyay, “Semidirect product of a monoid and a Γ-semigroup,” East-West Journal of Mathematics, vol. 6, no. 2, pp. 131–138, 2004. View at Google Scholar · View at MathSciNet
  18. M. K. Sen and A. Seth, “On po-Γ-semigroups,” Bulletin of the Calcutta Mathematical Society, vol. 85, no. 5, pp. 445–450, 1993. View at Google Scholar · View at MathSciNet
  19. M. K. Sen and N. K. Saha, “Orthodox Γ-semigroups,” International Journal of Mathematics and Mathematical Sciences, vol. 13, no. 3, pp. 527–534, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  20. Z. X. Zhong and M. K. Sen, “On several classes of orthodox Γ-semigroups,” Journal of Pure Mathematics, vol. 14, pp. 18–25, 1997. View at Google Scholar · View at MathSciNet
  21. A. Seth, “Γ-group congruences on regular Γ-semigroups,” International Journal of Mathematics and Mathematical Sciences, vol. 15, no. 1, pp. 103–106, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  22. S. K. Sardar, B. Davvaz, and S. K. Majumder, “A study on fuzzy interior ideals of Γ-semigroups,” Computers & Mathematics with Applications, vol. 60, no. 1, pp. 90–94, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  23. S. M. Anvariyeh, S. Mirvakili, and B. Davvaz, “On Γ-hyperideals in Γ-semihypergroups,” Carpathian Journal of Mathematics, vol. 26, no. 1, pp. 11–23, 2010. View at Google Scholar · View at MathSciNet
  24. S. M. Anvariyeh, S. Mirvakili, and B. Davvaz, “Pawlak's approximations in Γ-semihypergroups,” Computers & Mathematics with Applications, vol. 60, no. 1, pp. 45–53, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  25. D. Heidari, S. O. Dehkordi, and B. Davvaz, “Γ-semihypergroups and their properties,” University Politehnica of Bucharest Scientific Bulletin, Series A, vol. 72, no. 1, pp. 195–208, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. M. Koskas, “Groupoïdes, demi-hypergroupes et hypergroupes,” Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol. 49, pp. 155–192, 1970. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. D. Freni, “Une note sur le coeur d'un hypergroupe et sur la clôture β* de β,” Rivista di Matemàtica Pura ed Applicata, vol. 8, pp. 153–156, 1991. View at Google Scholar