Congruences on abundant semigroups associated with Green’s *-relations

Good congruences are defined as congruences preserving $$\mathcal L^*$$ -classes and $$\mathcal R^*$$ -classes. In this paper the good congruences on abundant semigroups generated by Green’s $$*$$ -relations are investigated. The related results for regular semigroups are enriched and extended.