Abstract. In 2003, G. Grätzer and E.$ $T. Schmidt introduced isoform lattices. A congruence relation on a lattice is {\it isoform}, if all the congruence classes are isomorphic sublattices. A lattice is {\it isoform}, if all of its congruences are isoform. They proved: {\it Every finite distributive lattice can be represented as the congruence lattice of a finite isoform lattice.} A much stronger result was proved by G. Grätzer, R.$ $W. Quackenbush, and E.$ $T. Schmidt in 2004: {\it Every finite lattice has a congruence-preserving extension to a finite isoform lattice.} They raised the problem whether this result can be extended to {\it congruence-finite} lattices, that is, to lattices with finitely many congruences. In this paper, we offer a positive solution of this problem, along with a somewhat easier proof of the original result.

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

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

Received July 20, 2007, and in revised form December 12, 2008. (Registered under 6057/2009.)