On the lattice of congruences on a regular semigroup
THOMAS E. HALL · Bulletin of the Australian Mathematical Society · 1969
A result of Reilly and Scheiblich for inverse semigroups is proved true also for regular semigroups. For any regular semigroup S the relation θ is defined on the lattice, Λ(S), of congruences on S by: (ρ, τ) ∈ θ if ρ and τ induce the same partition of the idempotents of S. Then θ is a congruence on Λ(S), Λ(S)/θ is complete and the natural homomorphism of Λ(S) onto Λ(S)/θ is a complete lattice homomorphism.