ACTA issues

Congruence-preserving extensions of finite lattices to isoform lattices

G. Gr├Ątzer, R. W. Quackenbush, E. T. Schmidt

Acta Sci. Math. (Szeged) 70:3-4(2004), 473-494

Abstract. We call a lattice $L$ {\it isoform}, if for any congruence relation $\Theta $ of $L$, all congruence classes of $\Theta $ 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: {\it Every finite lattice has a congruence-preserving extension to a finite isoform lattice}.

AMS Subject Classification (1991): 06B10, 06B15

Keyword(s): Congruence lattice, congruence-preserving extension, isoform, uniform

Received February 26, 2004. (Registered under 5826/2009.)