Topologically simple semihypergroup
Subject Areas : Topological Algebra
H.
Jafarabadi
1
(Department of Mathematics, Bardsir Branch, Islamic Azad University, Bardsir, Iran)
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.
[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.