ACTA issues

## Congruence-preserving extensions of finite lattices to isoform lattices

G. Grätzer, R. W. Quackenbush, E. T. Schmidt

Acta Sci. Math. (Szeged) 70:3-4(2004), 473-494
5826/2009

 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.)