Korean J. Math. Vol. 27 No. 1 (2019) pp.63-80
DOI: https://doi.org/10.11568/kjm.2019.27.1.63

On Corsini hypergroups and their productional hypergroups

Main Article Content

M. Al Tahan
Bijan Davvaz

Abstract

In this paper, we consider a special hypergroup defined by Corsini and we name it Corsini hypergroup. First, we investigate some of its properties and find a necessary and sufficient condition for the productional hypergroup of Corsini hypergroups to be a Corsini hypergroup. Next, we study its regular relations, fundamental group and complete parts. Finally, we characterize all Corsini hypergroups of orders two and three up to isomorphism.


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References

[1] M. Al- Tahan and B. Davvaz, On a special single-power cyclic hypergroup and its automorphisms, Discrete Mathematics, Algorithms and Applications 7 (4) (2016), 12 pages. Google Scholar

[2] M. Al- Tahan and B. Davvaz, On some properties of single power cyclic hypergroups and regular relations, J. Algebra Appl. 16 (11) (2017), 14 pages. Google Scholar

[3] R. Ameri, M. Amiri-Bideshki, A.B. Saeid and S. Hoskova-Mayerova, Prime filters of hyperlattices, An. Stiint. Univ. “Ovidius" Constanta Ser. Mat. 24(2) (2016), 15–26. Google Scholar

[4] R. Ameri, A. Kordi and S. Hoskova-Mayerova, Multiplicative hyperring of fractions and coprime hyperideals, An. Stiint. Univ. “Ovidius" Constanta Ser. Mat. 25(1) (2017), 5–23. Google Scholar

[5] P. Corsini, Prolegomena of Hypergroup Theory, Second edition, Aviani Editore, Italy, 1993. Google Scholar

[6] P. Corsini, Hypergraphs and hypergroups, Algebra Universalis 35 (4) (1996), 548–555. Google Scholar

[7] P. Corsini and V. Leoreanu, Applications of Hyperstructures Theory, Advances in Mathematics, Kluwer Academic Publisher, 2003. Google Scholar

[8] B. Davvaz, Polygroup Theory and Related Systems, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013. viii+200 pp. Google Scholar

[9] B. Davvaz, Semihypergroup Theory, Elsevier, 2016. Google Scholar

[10] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007. Google Scholar

[11] M. De Salvo and D. Freni, Cyclic semihypergroups and hypergroups, (Italian) Atti Sem. Mat. Fis. Univ. Modena 30 (1) (1981), 44–59. Google Scholar

[12] D. Freni, A note on the core of a hypergroup and the transitive closure β∗ of β, Riv. Mat. Pura Appl., 8 (1991), 153–156. Google Scholar

[13] S. Hoskova-Mayerova and A. Maturo, Algebraic hyperstructures and social relations, Ital. J. Pure Appl. Math. 39 (2018), 701–709. Google Scholar

[14] M. Koskas, Groupoides, demi-hypergroupes et hypergroupes, J. Math. Pure Appl. 49 (1970), 155–192. Google Scholar

[15] V. Leoreanu, About the simplifiable cyclic semihypergroups, Ital. J. Pure Appl. Math. 7 (2000), 69–76. Google Scholar

[16] F. Marty, Sur une generalization de la notion de group, In 8th Congress Math. Scandenaves, (1934), 45–49. Google Scholar

[17] J. Mittas, Hypergroups canoniques, Math. Balkanica 2 (1972), 165–179. Google Scholar

[18] S.Sh. Mousavi, V. Leoreanu-Fotea and M. Jafarpour, Cyclic groups obtained as quotient hypergroups, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 61 (1) (2015), 109–122. Google Scholar

[19] T. Vougiouklis, Hyperstructures and Their Representations, Aviani editor. Hadronic Press, Palm Harbor, USA, 1994. Google Scholar

[20] T. Vougiouklis, Cyclicity in a special class of hypergroups, Acta Univ. Carolin. Math. Phys. 22 (1) (1981), 3–6. Google Scholar