ACTA issues

Complete congruence representations with $2$-distributive modular lattices

G. Gr├Ątzer, E. T. Schmidt

Acta Sci. Math. (Szeged) 67:1-2(2001), 39-50

Abstract. In 1990, we published the following result: {\it Let $\eufm m$ be a regular cardinal $> \aleph_0$. Every {\rm $\eufm m$-algebraic lattice } $L$ can be represented as the lattice of $\eufm m$-complete congruence relations of an {\rm $\eufm m$-complete modular lattice } $K$.} In this note, we present a short proof of this theorem. In fact, we present a significant improvement: The lattice $K$ we construct is $2$-distributive.

AMS Subject Classification (1991): 06B10, 06D05

Keyword(s): Complete lattice, 2, -distributive lattice, complete congruence, congruence lattice

Received March 3, 2000. (Registered under 2772/2009.)