Czédli Gábor and Mureşan Claudia:
*On principal congruences and the number of congruences of a lattice with more ideals than filters.*
In: Acta scientiarum mathematicarum, (85) 3-4.
pp. 363-380. (2019)

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## Abstract

Let λ and κ be cardinal numbers such that κ is infinite and either2 ≤ λ ≤ κ, or λ = 2κ. We prove that there exists a lattice L exactly λ many congruences ,2κ many ideals, but only κ many filters. Furthermore, if λ ≤ 2isan integer of the form 2m·3n, then we can choose L to be a modular lattice generating one of the minimal modular nondistributive congruence varieties described by Ralph Freese in 1976, and this L is even relatively complemented for λ= 2. Related to some earlier results of George Grätzer and the first author,we also prove that ifPis a bounded ordered set (in other words, a boundedposet) with at least two elements,G is a group, and κ is an infinite cardinal such that κ≥ |P|and κ≥ |G|, then there exists a lattice L of cardinality κ that (i) the principal congruences of L form an ordered set isomorphic to P, (ii) the automorphism group of L is isomorphic to G, (iii)L has 2κ many ideals, but (iv)L has only κ many filters.

Item Type: | Article |
---|---|

Journal or Publication Title: | Acta scientiarum mathematicarum |

Date: | 2019 |

Volume: | 85 |

Number: | 3-4 |

ISSN: | 2064-8316 |

Page Range: | pp. 363-380 |

Related URLs: | http://acta.bibl.u-szeged.hu/66425/ |

DOI: | 10.14232/actasm-018-538-y |

Uncontrolled Keywords: | Rácselmélet - rács szűrő - egyezések |

Additional Information: | Ábrákkal ill. Bibliogr.: p. 378-380. |

Date Deposited: | 2020. Apr. 23. 11:02 |

Last Modified: | 2021. Mar. 25. 15:34 |

URI: | http://acta.bibl.u-szeged.hu/id/eprint/66321 |

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