%0 Journal Article
%T Fundamental relations in simple and 0-simple semihypergroups of small size
%A Dario Fasino
%A Domenico Freni
%J Arabian Journal of Mathematics
%@ 2193-5351
%D 2012
%I 
%R 10.1007/s40065-012-0025-2
%X We consider the fundamental relations ¦Â and ¦Ã in simple and 0-simple semihypergroups, especially in connection with certain minimal cardinality questions. In particular, we enumerate and exhibit all simple and 0-simple semihypergroups having order 3 where ¦Â is not transitive, apart of isomorphisms. Moreover, we show that the least order for which there exists a strongly simple semihypergroup where ¦Â is not transitive is 4. Finally, we prove that ¦Ã is transitive in all simple semihypergroups, and determine necessary and sufficient conditions for a 0-simple semihypergroup to have ¦Ã transitive. The latter results obviously hold also for simple and 0-simple semigroups.
%K 20N20
%K 05A99
%U http://link.springer.com/article/10.1007/s40065-012-0025-2