A generalization of the Hall semigroup of a band

Abstract

AbstractLet E be a band and ε a compatible partition on it. If S is an orthodox semigroup with band of idempotents E such that there exists a congruence on S inducing the partition ε then we define a homomorphism of S into a Hall semigroup whose kernel is the greatest congruence on S inducing the partition ε. On the other hand, we define a subsemigroup of the Hall semigroup WE possessing the property that S is an othodox semigroup with band of idempotents E which has a congruence inducing ε if and only if the range of the Hall homomoprhism of S into WE is contained in .