Two-sided networks for completely simple semigroups

Let S be a completely simple semigroup represented as a Rees matrix semigroup M(I,G,P) with normalized sandwich matrix P. On the congruence lattice C(S) of S we consider the relations T i, K and T r which identify congruences with the same left trace, kernel and right trace, respectively. These are equivalences whose classes are intervals. The upper and lower ends of these intervals induce the following operators on C(S) Tl, K, Tr, tl, k and tr .We construct here the semigroup generated by these operators as a homomorphic image of a semigroup given by generators and relations and demonstrate the minimality of the latter.