Korean J. Math. Vol. 28 No. 3 (2020) pp.421-438
DOI: https://doi.org/10.11568/kjm.2020.28.3.421

Commutative single power cyclic hypergroups of order 4 and period 2

Main Article Content

M.R. Kheradmand
Bijan Davvaz

Abstract

In this paper we enumerate all commutative single power cyclic hypergroups of order 4 and period 2. Moreover, we prove some interesting properties regarding cyclic hypergroups.



Article Details

References

[1] M. Al Tahan and B. Davvaz, On a special single- power cyclic hypergroup and its automorphisms, Discrete Mathematics, Algorithms and Applications, 8 (4) (2016) 1650059 (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), 1750214, 14 pp. Google Scholar

[3] M. Al Tahan and B. Davvaz, Hypermatrix representations of single power cyclic hypergroups, Ital. J. Pure Appl. Math. 38 (2017) 679–696. Google Scholar

[4] M. Al Tahan and B. Davvaz, Commutative single power cyclic hypergroups of order three and period two, Discrete Mathematics, Algorithms and Applications (DMAA), 19 (5) (2017), 1750070 (15 pages). Google Scholar

[5] M. Al Tahan, S. Hoskova-Mayerova and B. Davvaz, An overview of topological hypergroupoids, Journal of Intelligent and Fuzzy Systems 34 (3) (2018) 1907– 1916. Google Scholar

[6] N. Antampoufis and S. Hoskova-Mayerova, A brief survey on the two different approaches of fundamental equivalence relations on hyperstructures, Ratio Mathematica 33 (2017) 47–60. Google Scholar

[7] P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, 1993, 216 pp. Google Scholar

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

[9] B. Davvaz, Semihypergroup Theory, Elsevier/Academic Press, London, 2016, viii+156 pp. Google Scholar

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

[11] D. Freni, Cyclic hypergroups and torsion in hypergroups, Matematiche (Catania) 35 (1-2) (1980), 270–286. Google Scholar

[12] S. Hoskova-Mayerova and A. Maturo, Algebraic hyperstructures and social relations, Italian Journal of Pure and Applied Mathematics 39 (2018), 701–709. Google Scholar

[13] L. Konguetsof, T. Vougiouklis, M. Kessoglides and S. Spartalis, On cyclic hypergroups with period, Acta Univ. Carolin. Math. Phys. 28 (1) (1987), 3–7. Google Scholar

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

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

[16] S. Mirvakili, P. Ghiasvand and B. Davvaz, Cyclic modules over fundamental rings derived from strongly regular equivalences, Annales mathematiques du Que- bec 41 (2017) 265–276. Google Scholar

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

[18] S.S. 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] M. Novak, S. Krehlik and I. Cristea, Cyclicity in EL Hypergroups, Symmetry 10 (11) (2018) 611; doi:10.3390/sym10110611 Google Scholar

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

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