"Complete-Simple" Distributive Lattices
George Grätzer, E. T. Schmidt · Proceedings of the American Mathematical Society · 1993
It is well known that the only simple distributive lattice is the twoelement chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences.. In this paper we show the existence of infinite complete-simple distributive lattices.