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 |

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Category: | math |

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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 |

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Date available: | 2014-09-29T09:42:07Z |

Last updated: | 2016-04-07 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/143954 |

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