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.)
|