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An extension theorem for planar semimodular lattices

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Abstract

We prove that every finite distributive lattice \(D\) can be represented as the congruence lattice of a rectangular lattice \(K\) in which all congruences are principal. We verify this result in a stronger form as an extension theorem.

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Authors and Affiliations

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

    G. Grätzer

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

    E. T. Schmidt

Authors
  1. G. Grätzer
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  2. E. T. Schmidt
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Corresponding author

Correspondence to E. T. Schmidt.

Additional information

To Lászlo Fuchs, our teacher, on his 90th birthday.

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Grätzer, G., Schmidt, E.T. An extension theorem for planar semimodular lattices. Period Math Hung 69, 32–40 (2014). https://doi.org/10.1007/s10998-014-0035-2

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  • DOI: https://doi.org/10.1007/s10998-014-0035-2

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