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

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.


Keywords


commutative single power, cyclic hypergroups.

Subject classification

20N20.

Sponsor(s)



Full Text:

PDF

References


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)

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)

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

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)

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)

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)

P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, 1993, 216 pp. (Google Scholar)

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

B. Davvaz, Semihypergroup Theory, Elsevier/Academic Press, London, 2016, viii+156 pp. (Google Scholar)

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

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

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

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)

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

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

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)

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

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)

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

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

T. Vougiouklis, Hyperstructures and Their Representations, Hadronic Press, Palm Harbor, USA, 1994. (Google Scholar)


Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr