Displaying similar documents to “The 0-distributivity in the class of subalgebra lattices of Heyting algebras and closure algebras”

Congruence lattices in varieties with compact intersection property

Filip Krajník, Miroslav Ploščica (2014)

Czechoslovak Mathematical Journal

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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 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...