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Finitely Presented Lattices: Continuity and Semidistributivity

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Lattices, Semigroups, and Universal Algebra

Abstract

In [3] we investigated finitely presented lattices and the closely related subject of lattices generated by a finite partial lattice. We described a canonical form for the elements of such a lattice and used this to study the covering relation. We showed that there is an effective procedure for finding the covers of any element of a finitely presented lattice. We gave an example of a finitely presented lattice which has no cover at all.

This research was partially supported by NSF grant no. DMS-8521710.

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References

  1. P. Crawley and R. P. Dilworth, “Algebraic Theory of Lattices”, Prentice-Hall, Englewood Cliffs, NJ, 1973.

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Author information

Authors and Affiliations

  1. University of Hawaii, Honolulu, HI, 96822, USA

    Ralph Freese

Authors
  1. Ralph Freese
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Editor information

Editors and Affiliations

  1. University of Porto, Porto, Portugal

    Jorge Almeida

  2. University of Lisbon, Lisbon, Portugal

    Gabriela Bordalo

  3. University of Illinois at Chicago, Chicago, Illinois, USA

    Philip Dwinger

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© 1990 Springer Science+Business Media New York

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Freese, R. (1990). Finitely Presented Lattices: Continuity and Semidistributivity. In: Almeida, J., Bordalo, G., Dwinger, P. (eds) Lattices, Semigroups, and Universal Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2608-1_7

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  • DOI: https://doi.org/10.1007/978-1-4899-2608-1_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-2610-4

  • Online ISBN: 978-1-4899-2608-1

  • eBook Packages: Springer Book Archive

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