Congruence lattices of regular semigroups related to kernels and traces
Mario Petrich · Proceedings of the Edinburgh Mathematical Society · 1991
The kernel–trace approach to congruences on a regular semigroupScan be refined by introducing the left and right traces. This induces eight operators on the lattice of congruences onS:t1,k, tr,;Tt,K,Tr;t,T. We describe the lattice of congruences onSgenerated by six 3-element subsets of the set {ωt1, ωk, ωtr, εTt, εK, εTr} where ω and ε denote the universal and the equality relations. This is effected by means of a diagram and in terms of generators and relations on a free distributive lattice, or a homomorphic image thereof. We perform the same analysis for the lattice of congruences onSgenerated by the set {εK, ωk, εT, ωt}.