CONGRUENCE NETWORKS FOR COMPLETELY SIMPLE SEMIGROUPS

The operators K, k, T and t are defined on the lattice C(S) of congruences on a Rees matrix semigroup S as follows. For rho is-an-element-of C(S), rhoK and rhok (rhoT and rhot) are the greatest and the least congruences with the same kernel (trace) as rho, respectively. We determine the semigroup generated by the operators K, k, T and t as they act on all completely simple semigroups. We also determine the network of congruences associated with a congruence rho is-an-element-of C(S) and the lattice generated by it. The latter is then represented by generators and relations.