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Lattice-ordered pregroups are semi-distributive

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Abstract

We prove that the lattice reduct of every lattice-ordered pregroup is semidistributive. This is a consequence of a certain weak form of the distributive law which holds in lattice-ordered pregroups.

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Acknowledgements

The authors are grateful to the anonymous referee for their careful reading of the manuscript and helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Denver, Denver, CO, 80208, USA

    Nick Galatos & Michael Kinyon

  2. Mathematics Chapman University, Orange, CA, 92866, USA

    Peter Jipsen

  3. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Adam Přenosil

Authors
  1. Nick Galatos
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  2. Peter Jipsen
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  3. Michael Kinyon
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  4. Adam Přenosil
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Correspondence to Adam Přenosil.

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Presented by W. Wm. McGovern.

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Galatos, N., Jipsen, P., Kinyon, M. et al. Lattice-ordered pregroups are semi-distributive. Algebra Univers. 82, 16 (2021). https://doi.org/10.1007/s00012-020-00703-4

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  • DOI: https://doi.org/10.1007/s00012-020-00703-4

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