Two congruence lattices of completely simple semigroups

Abstract

Abstract. For a Rees matrix semigroup S with normalized sandwich matrix and p6cg(S), the congruence lattice of S, we consider the lattice generated by {pT~, pK, pT,, pfi, pk, ptr}. Here pT~ and pt~ are the upper and lower ends of the interval which makes up the J'rclass of p, 3-t being the left trace relation on cg(S). The remaining symbols have the analogous meaning relative to the kernel and the right trace relations. We also consider the lattice generated by {~Tl, eK,~T,,cotjOk,~Ot,} where e and ~o are the equality and the universal relations on S, respectively. In both cases, we find lattices "freest" relative to these lattices and represent them as distributive lattices with generators and relations.