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A note on congruence lattices of slim semimodular lattices

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Abstract

Recently, G. Grätzer has raised an interesting problem: Which distributive lattices are congruence lattices of slim semimodular lattices? We give an eight element slim distributive lattice that cannot be represented as the congruence lattice of a slim semimodular lattice. Our lattice demonstrates the difficulty of the problem.

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Authors and Affiliations

  1. University of Szeged, Bolyai Institute, Aradi vértanúk tere 1, Szeged, 6720, Hungary

    Gábor Czédli

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  1. Gábor Czédli
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Correspondence to Gábor Czédli.

Additional information

Presented by G. Gratzer.

This research was supported by the European Union and co-funded by the European Social Fund under the project “Telemedicine-focused research activities on the field of Mathematics, Informatics and Medical sciences” of project number “TÁMOP-4.2.2.A- 11/1/KONV-2012-0073”, and by NFSR of Hungary (OTKA), grant number K83219.

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Czédli, G. A note on congruence lattices of slim semimodular lattices. Algebra Univers. 72, 225–230 (2014). https://doi.org/10.1007/s00012-014-0286-z

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  • DOI: https://doi.org/10.1007/s00012-014-0286-z

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