Congruence-preserving extensions of finite lattices to isoform lattices
George Grätzer, Robert W. Quackenbush, E. T. Schmidt · 2004
We call a lattice L isoform, if for any congruence relation Θ of L, all congruence classes of Θ are isomorphic sublattices. In an earlier paper, we proved that for every finite distributive lattice D, there exists a finite isoform lattice L such that the congruence lattice of L is isomorphic to D. In this paper, we prove a much stronger result: Every finite lattice has a congruence-preserving extension to a finite isoform lattice.