On bisimple semigroups generated by a finite number of idempotents

Abstract

Non-completely simple bisimple semigroups 5 which are generated by a finite number of idempotents are studied by means of Rees matrix semigroups over local submonoids eSe, e = e 2 G S. If under the natural partial order on the set £ ( of idempotents of such a semigroup S the sets u(e) = {/ G E s : f =s e) for each e G E s are well-ordered, then S is shown to contain a subsemigroup isomorphic to Sp 4 , the fundamental four-spiral semigroup. A non-completely simple bisimple semigroup is constructed which is generated by 5 idempotents but which does not contain a subsemigroup isomorphic to S/) 4 .