Geodesic
Congruence lattices in varieties with compact intersection property
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 115-132
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We say that a variety ${\mathcal V}$ of algebras has the Compact Intersection Property (CIP), if the family of compact congruences of every $A\in {\mathcal V}$ 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 ${\mathcal V}$ and embeddings between them. We believe that the strategy used here can be further developed and used to describe the congruence lattices for any (locally finite) congruence-distributive CIP variety.
We say that a variety ${\mathcal V}$ of algebras has the Compact Intersection Property (CIP), if the family of compact congruences of every $A\in {\mathcal V}$ 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 ${\mathcal V}$ and embeddings between them. We believe that the strategy used here can be further developed and used to describe the congruence lattices for any (locally finite) congruence-distributive CIP variety.
DOI : 10.1007/s10587-014-0088-7
Classification : 06D15, 08A30, 08B10
Keywords: compact congruence; congruence-distributive variety 
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Krajník, Filip; Ploščica, Miroslav. Congruence lattices in varieties with compact intersection property. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 115-132. doi: 10.1007/s10587-014-0088-7

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