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, Volume 35, Issue 1, pp 133–137 | Cite as

Interval Dismantlable Lattices

  • Kira Adaricheva
  • Jennifer Hyndman
  • Steffen Lempp
  • J. B. Nation
Article

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.

Keywords

Lattice Join prime Meet prime Generating set Quasivariety 

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References

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Kira Adaricheva
    • 1
  • Jennifer Hyndman
    • 2
  • Steffen Lempp
    • 3
  • J. B. Nation
    • 4
  1. 1.Department of MathematicsHofstra UniversityHempsteadUSA
  2. 2.Department of Mathematics and StatisticsUniversity of Northern British ColumbiaPrince GeorgeCanada
  3. 3.Department of MathematicsUniversity of WisconsinMadisonUSA
  4. 4.Department of MathematicsUniversity of HawaiiHonoluluUSA

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