| 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:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143954 |
| . |
| Reference:
|
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