Congruence lattices in varieties with compact intersection property

Krajník, Filip, and Ploščica, Miroslav. "Congruence lattices in varieties with compact intersection property." Czechoslovak Mathematical Journal 64.1 (2014): 115-132. <http://eudml.org/doc/261982>.

@article{Krajník2014,
abstract = {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.},
author = {Krajník, Filip, Ploščica, Miroslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {compact congruence; congruence-distributive variety; compact congruences; congruence-distributive varieties; congruence lattices; CIP varieties; subdirectly irreducible algebras},
language = {eng},
number = {1},
pages = {115-132},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Congruence lattices in varieties with compact intersection property},
url = {http://eudml.org/doc/261982},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Krajník, Filip
AU - Ploščica, Miroslav
TI - Congruence lattices in varieties with compact intersection property
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 115
EP - 132
AB - 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.
LA - eng
KW - compact congruence; congruence-distributive variety; compact congruences; congruence-distributive varieties; congruence lattices; CIP varieties; subdirectly irreducible algebras
UR - http://eudml.org/doc/261982
ER -