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arXiv · 1303.4464

A short proof of the congruence representation theorem for semimodular lattices

G. Grätzer·E. T. Schmidt
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Abstract

In a 1998 paper with H. Lakser, the authors proved that every finite distributive lattice $D$ can be represented as the congruence lattice of a finite \emph{semimodular lattice}. Some ten years later, the first author and E. Knapp proved a much stronger result, proving the representation theorem for \emph{rectangular lattices}. In this note we present a short proof of these results.

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G. Grätzer, E. T. Schmidt. 2013-03-19. A short proof of the congruence representation theorem for semimodular lattices. https://arxiv.org/abs/1303.4464

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