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Algebra universalis

, 79:21 | Cite as

Some preliminary results on the set of principal congruences of a finite lattice

  • G. Grätzer
  • H. Lakser
Article
Part of the following topical collections:
  1. In memory of Bjarni Jónsson

Abstract

In the second edition of the congruence lattice book, Problem 22.1 asks for a characterization of subsets Q of a finite distributive lattice D such that there is a finite lattice L whose congruence lattice is isomorphic to D and under this isomorphism Q corresponds the the principal congruences of L. In this note, we prove some preliminary results.

Keywords

Congruence lattice Principal congruence Join-irreducible congruence Principal congruence representable set 

Mathematics Subject Classification

06B10 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ManitobaWinnipegCanada

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