Representation of lattices by congruence lattices of semigroups without idempotents

It is proved that every distributive algebraic lattice such that its compact elements form a lattice with unit can be represented as the congruence lattice of some semigroup without idempotents. This implies that every distributive algebraic lattice with at most countably many compact elements is also representable as the congruence lattice of a semigroup without idempotents.