English

A short proof of the congruence representation theorem for semimodular lattices

Rings and Algebras 2019-08-13 v2

Abstract

In a 1998 paper with H. Lakser, the authors proved that every finite distributive lattice DD 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.

Keywords

Cite

@article{arxiv.1303.4464,
  title  = {A short proof of the congruence representation theorem for semimodular lattices},
  author = {G. Grätzer and E. T. Schmidt},
  journal= {arXiv preprint arXiv:1303.4464},
  year   = {2019}
}