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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada

    G. Grätzer & H. Lakser

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  1. G. Grätzer
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  2. H. Lakser
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Correspondence to G. Grätzer.

Additional information

Presented by J.B. Nation.

To the memory of our friend of more than 50 years, Bjarni Jónsson.

This article is part of the topical collection “In memory of Bjarni Jónsson” edited by J.B. Nation.

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Grätzer, G., Lakser, H. Some preliminary results on the set of principal congruences of a finite lattice. Algebra Univers. 79, 21 (2018). https://doi.org/10.1007/s00012-018-0487-y

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  • DOI: https://doi.org/10.1007/s00012-018-0487-y

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