Right group congruences on a semigroup

Abstract

This paper develops necessary and sufficient conditions on an algebraic semigroup S in order that it will have nontrivial right group homomorphic images. A central notion used is that of how the normal subsemigroups associated with the group images of S relate to the right group images of S. The results presented thus extend those of R. R. Stoll. Where right group congruences exist, the structure of S is determined and the right group congruences are characterized in terms of group congruences and right zero congruences on S. Sufficient conditions are then found for the existence of a minimum right group congruence on S, and isomorphic right group congruences and the minimum right group congruence on S are described. Lastly, an application is made to regular semigroups whose idempotents form a rectangular band.