Congruence-free right simple semigroups
Peter G. Trotter · Journal of the Australian Mathematical Society · 1977
Abstract Congruence-free right simple semigroups with idempotents are simple groups or have order 2. It is shown in this paper that there exist congruence-free simple semigroups without idempotents. Some properties of congruences on right simple semigroups, expressed mainly in terms of their unitary and left unitary subsemigroups, are determined. These are used to provide characterizations of congruence-free right simple semigroups.