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A short proof of the congruence representation theorem of rectangular lattices

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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 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.

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References

  1. G. Czédli and G. Grätzer: Planar Semimodular Lattices: Structure and Diagrams. In: G. Grätzer and F. Wehrung (eds.) Lattice Theory: Empire. Special Topics and Applications. Birkhäuser Verlag, Basel (2013)

  2. G. Grätzer: Planar Semimodular Lattices: Congruences. In: G. Grätzer and F. Wehrung (eds.) Lattice Theory: Empire. Special Topics and Applications. Birkhäuser Verlag, Basel (2013)

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Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada

    G. Grätzer

  2. Mathematical Institute of the Budapest University of Technology and Economics, H-1521, Budapest, Hungary

    E. T. Schmidt

Authors
  1. G. Grätzer
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  2. E. T. Schmidt
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Correspondence to G. Grätzer.

Additional information

Presented by G. Czedli.

The second author was supported by the Hungarian National Foundation for Scientific Research (OTKA), grant no. K77432.

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Grätzer, G., Schmidt, E.T. A short proof of the congruence representation theorem of rectangular lattices. Algebra Univers. 71, 65–68 (2014). https://doi.org/10.1007/s00012-013-0264-x

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  • DOI: https://doi.org/10.1007/s00012-013-0264-x

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