Notes on planar semimodular lattices. VIII. Congruence lattices of SPS lattices

2021/04/28 by George Grätzer, Grätzer, G.
Computer Science · Decision Sciences · #06D05 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2104.13843

openalex publication_date 2021/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, I find a new property of the congruence lattice, ConL, of an SPS lattice L (slim, planar, semimodular, where "slim" is the absence of~\mathsf M₃ sublattices) with more than 2 elements: there are at least two dual atoms in ConL. So the three-element chain cannot be represented as the congruence lattice of an SPS lattice, supplementing a~result of G. Czédli.

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