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Congruence lattices in varieties with compact intersection property

Filip Krajník; Miroslav Ploščica — 2014

Czechoslovak Mathematical Journal

We say that a variety $𝒱$ of algebras has the Compact Intersection Property (CIP), if the family of compact congruences of every $A \in 𝒱$ is closed under intersection. We investigate the congruence lattices of algebras in locally finite, congruence-distributive CIP varieties and obtain a complete characterization for several types of such varieties. It turns out that our description only depends on subdirectly irreducible algebras in $𝒱$ and embeddings between them. We believe that the strategy used here can...

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