Congruences On Abundant Semigroups

In this thesis, we investigate the congruences on abundant semigroups associated with Green's *-relations. Good congruences are defined as con-gruences preserving L*-classes and R*-classes. The thesis is divided into five sections.After providing some preliminaries and some notations of abundan-t semigroup in Section 2, we consider the good congruences on abundant semigroups generated by Green's *-relations in Section 3.we study the good congruences on abundant semigroups satisfying the regularity condition gen-erated by L*|E,R*|E,D*|E in Section 4. finally, we consider the special case: concordant semigroups.