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Title: Congruence lattices in varieties with compact intersection property (English)
Author: Krajník, Filip
Author: Ploščica, Miroslav
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 64
Issue: 1
Year: 2014
Pages: 115-132
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: compact congruence
Keyword: congruence-distributive variety
MSC: 06D15
MSC: 08A30
MSC: 08B10
idZBL: Zbl 06391481
idMR: MR3247449
DOI: 10.1007/s10587-014-0088-7
Date available: 2014-09-29T09:42:07Z
Last updated: 2016-04-07
Stable URL:
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