Embedding any countable semigroup without idempotents in a 2-generated simple semigroup without idempotents

Abstract

Although the classes of regular simple semigroups and simple semigroups without idempotents are evidently at opposite ends of the spectrum of simple semigroups, their theories involve some interesting connections. Jones [5] has obtained analogues of the bicyclic semigroup for simple semigroups without idempotents. Megyesi and Pollák [7] have classified all combinatorial simple principal ideal semigroups on two generators, showing that all are homomorphic images of one such semigroup Po which has no idempotents.