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Interval Dismantlable Lattices

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Abstract

A finite lattice is interval dismantlable if it can be partitioned into an ideal and a filter, each of which can be partitioned into an ideal and a filter, etc., until you reach 1-element lattices. In this note, we find a quasi-equational basis for the pseudoquasivariety of interval dismantlable lattices, and show that there are infinitely many minimal interval non-dismantlable lattices.

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Authors and Affiliations

  1. Department of Mathematics, Hofstra University, Hempstead, NY, 11549, USA

    Kira Adaricheva

  2. Department of Mathematics and Statistics, University of Northern British Columbia, Prince George, BC, Canada

    Jennifer Hyndman

  3. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Steffen Lempp

  4. Department of Mathematics, University of Hawaii, Honolulu, HI, 96822, USA

    J. B. Nation

Authors
  1. Kira Adaricheva
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  2. Jennifer Hyndman
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  3. Steffen Lempp
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  4. J. B. Nation
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Correspondence to J. B. Nation.

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Adaricheva, K., Hyndman, J., Lempp, S. et al. Interval Dismantlable Lattices. Order 35, 133–137 (2018). https://doi.org/10.1007/s11083-017-9422-7

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  • DOI: https://doi.org/10.1007/s11083-017-9422-7

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