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Compact Intersection Property and description of congruence lattices

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Mathematica Slovaca

Abstract

We say that a variety V of algebras has the Compact Intersection Property (CIP), if the family of compact congruences of every A ∈ V is closed under intersection. We investigate the congruence lattices of algebras in locally finite congruence-distributive CIP varieties. We prove some general results and obtain a complete characterization for some types of such varieties. We provide two kinds of description of congruence lattices: via direct limits and via Priestley duality.

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Authors and Affiliations

  1. Institute of Mathematics, Šafárik’s University, Jesenná 5, SK-041 54, Košice, Slovakia

    Filip Krajník

  2. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, SK-040 01, Košice, Slovakia

    Miroslav Ploščica

Authors
  1. Filip Krajník
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  2. Miroslav Ploščica
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Corresponding author

Correspondence to Filip Krajník.

Additional information

Communicated by Anatolij Dvurečenskij

Dedicated to Professor Ján Jakubík on the occasion of his 90th birthday

Supported by VEGA Grant 2/0194/10.

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Krajník, F., Ploščica, M. Compact Intersection Property and description of congruence lattices. Math. Slovaca 64, 643–664 (2014). https://doi.org/10.2478/s12175-014-0231-9

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  • DOI: https://doi.org/10.2478/s12175-014-0231-9

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