A short proof of the congruence representation theorem for semimodular lattices

2013/03/19 by George Grätzer, Grätzer, G., E. T. Schmidt +1
Computer Science · Decision Sciences · #Advanced Algebra and Logic #FOS: Mathematics #Multi-Criteria Decision Making #Primary: 06B10. Secondary: 06A06 #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1303.4464

openalex publication_date 2013/03/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 semimodular lattice. Some ten years later, the first author and E. Knapp proved a much stronger result, proving the representation theorem for rectangular lattices. In this note we present a short proof of these results.

Citations

• The order of principal congruences of a semimodular lattice

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