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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 64, Issue 3


Compact Intersection Property and description of congruence lattices

Filip Krajník / Miroslav Ploščica
Published Online: 2014-07-05 | DOI: https://doi.org/10.2478/s12175-014-0231-9


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.

MSC: Primary 08A30; Secondary 08A10, 06D15

Keywords: compact congruence; congruence-distributive variety

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About the article

Published Online: 2014-07-05

Published in Print: 2014-06-01

Citation Information: Mathematica Slovaca, Volume 64, Issue 3, Pages 643–664, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-014-0231-9.

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© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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