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Congruence structure of planar semimodular lattices: the General Swing Lemma

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Abstract

The Swing Lemma, proved by G. Grätzer in 2015, describes how a congruence spreads from a prime interval to another in a slim (having no \(\mathsf {M}_{3}\) sublattice), planar, semimodular lattice. We generalize the Swing Lemma to planar semimodular lattices.

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Authors and Affiliations

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

    Gábor Czédli

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

    George Grätzer & Harry Lakser

Authors
  1. Gábor Czédli
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  2. George Grätzer
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  3. Harry Lakser
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Corresponding author

Correspondence to George Grätzer.

Additional information

Presented by F. Wehrung.

To the memory of E. T. Schmidt.

This article is part of the topical collection “In memory of E. Tamás Schmidt” edited by Robert W. Quackenbush.

This research was supported by NFSR of Hungary (OTKA), Grant Number K 115518.

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Czédli, G., Grätzer, G. & Lakser, H. Congruence structure of planar semimodular lattices: the General Swing Lemma. Algebra Univers. 79, 40 (2018). https://doi.org/10.1007/s00012-018-0483-2

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  • DOI: https://doi.org/10.1007/s00012-018-0483-2

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