Idempotent-connected abundant semigroups
Abdulsalam El-Qallali, John Fountain · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1981
Synopsis A general theory for a class of abundant semigroups is developed. For a semigroup S in this class let E be its set of idempotents and the subsemigroup of S generated by E. When is regular there is a homomorphism with a number of desirable properties from S onto a full subsemigroup of the Hall semigroup T . From this fact, analogues of results in the regular case are obtained for *-simple and ℐ*-simple abundant semigroups.