A short proof of the congruence representation theorem of rectangular lattices. (Q2449449)

In a 1988 paper the authors together with \textit{H. Lakser} [Can. Math. Bull. 41, No. 3, 290--297 (1998; Zbl 0918.06004)] proved that every finite distributive lattice \(D\) can be represented as the congruence lattice of a finite semimodular lattice. Later on, the first author and \textit{E. Knapp} [Acta Sci. Math. 75, No. 1--2, 29--48 (2009; Zbl 1199.06029)] proved a much stronger result substituting semimodularity by rectangularity. The aim of the paper is to present a short proof of these results.