On the lattice of congruences on a semilattice
THOMAS E. HALL · Journal of the Australian Mathematical Society · 1971
Lattices of congruences are studied in section II.6 of Cohn [2]. Papers [5] and [6] by Munn deal with lattices of congruences on semigroups and conditions under which these lattices are modular. In [4] Lallement shows that the lattice of congruences on a completely 0-simple semigroup is semimodular, giving an alternative proof of the result, due to Preston [7], that the lattice of congruences on a completely 0-simple semigroup satisfies a certain chain condition which is a natural extension to arbitrary lattices of the Jordan-Dedekind chain condition for finite lattices.