Congruence lattices in varieties with compact intersection property

Title:

Congruence lattices in varieties with compact intersection property

Creator:

Krajník, Filip and Ploščica, Miroslav

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a4c46abb-08e3-4160-b9f9-0fc5cac49cdc
uuid:a4c46abb-08e3-4160-b9f9-0fc5cac49cdc

Subject:

compact congruence and congruence-distributive variety

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

115-132

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:1

Harvested from:

CDK

Metadata only:

false