Finite semigroups with commuting idempotents
C. J. Ash, THOMAS E. HALL · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1987
Abstract We show that every such semigroup is a homomorphic image of a subsemigroup of some finite inverse semigroup. This shows that the pseudovariety generated by the finite inverse semigroups consists of exactly the finite semigroups with commuting idempotents.