Topologically simple semihypergroup

Subject Areas : Topological Algebra

H. Jafarabadi ¹

1 - Department of Mathematics, Bardsir Branch, Islamic Azad University, Bardsir, Iran

Received: 2022-08-15 Accepted : 2022-09-30 Published : 2022-09-01

Keywords: Hypergroupoid, hypergroup, semihypergroip, simple semihypergroup, topological semihypergroup,

Abstract :

In this note, we introduce the concept of topologically simple semihypergroup and determine when topological simplicity of a complete subsemihypergroup of a semihypergroup implies its simplicity from algebraic point of view.

References:

[1] N. Abbasizadeh, B. Davvaz, Intuitionistic fuzzy topological polygroups, Int. J. Anal. Appl. 12 (2) (2016), 163-179.

[2] R. Ameri, Topological transposition hypergroups, Ital. J. Pure Appl. Math. 13 (2003), 171-176.

[3] P. Corsini, V. Leoreanu, Applications of Hyperstructures Theory, Dordrecht, Kluwer Academic Publisher, 2003.

[4] I. Cristea, S. Hoskova, Fuzzy pseudotopological hypergroupoids, Iran. J. Fuzzy Syst. 6 (4) (2009), 11-19.

[5] D. Heidari, B. Davvaz, S. Modarres, Topological hypergroups in the sense of Marty, Commun. Algebra. 42 (2014), 4712-4721.

[6] D. Heidari, B. Davvaz, S. Modarres, Topological polygroups, Bull. Malays. Math. Sci. Soc. 39 (2) (2016), 707-721.

[7] S. Hoskava-Mayerova, Topological hypergroupoid, Comput. Math. Appl. 64 (2012), 2845-2849.

[8] H. M. Jafarabadi, N. H. Sarmin, M. R. Molaei, Completely simple and regular semihypergroups, Bull. Malays. Math. Sci. Soc. 35 (2) (2012), 335-343.

[9] S. Manoranjan, D. Kousik, B. Davvaz, On topological complete hypergroups, Filomat. 31 (16) (2017), 5045-5056.

[10] F. Marty, Sur Uni Generalization de la Notion de Group, 8th Congress Math Scandenaves, Stockholm, 1934.

[11] M. S. Shadkami, M. R. Ahmadi, B. Davvaz, The role of complete part in topological polygroups, Int. J. Anal. Appl. 11 (2016), 54-60.

[12] H. S. Wall, Hypergroups, Amer. J. Math. 59 (1937), 77-98.