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Canonical extensions, free completely distributive lattices, and complete retracts

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Abstract

We provide a simple proof of a recent result of Morton and van Alten that the canonical extension of a bounded distributive lattice is its free completely distributive extension. We show that this can be used to easily obtain a number of results, both known and new.

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Acknowledgements

We are thankful to the referees for comments that have improved the note, and to one referee for pointing out that the key observation of Theorem 2.1 is in print.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, USA

    Guram Bezhanishvili & John Harding

  2. TSU Razmadze Mathematical Institute, 0186, Tbilisi, Georgia

    Mamuka Jibladze

Authors
  1. Guram Bezhanishvili
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  2. John Harding
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  3. Mamuka Jibladze
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Corresponding author

Correspondence to Guram Bezhanishvili.

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Presented by N. Galatos.

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John Harding was partially supported by ARL grant W911NF-21-1-0247.

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Bezhanishvili, G., Harding, J. & Jibladze, M. Canonical extensions, free completely distributive lattices, and complete retracts. Algebra Univers. 82, 64 (2021). https://doi.org/10.1007/s00012-021-00756-z

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  • DOI: https://doi.org/10.1007/s00012-021-00756-z

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