On principal congruences and the number of congruences of a lattice with more ideals than filters
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 gener...
Elmentve itt :
| Szerzők: | |
|---|---|
| Dokumentumtípus: | Cikk |
| Megjelent: |
2019
|
| Sorozat: | Acta scientiarum mathematicarum
85 No. 3-4 |
| Kulcsszavak: | Rácselmélet - rács szűrő - egyezések |
| doi: | 10.14232/actasm-018-538-y |
| Online Access: | http://acta.bibl.u-szeged.hu/66321 |
| LEADER | 01779nab a2200217 i 4500 | ||
|---|---|---|---|
| 001 | acta66321 | ||
| 005 | 20210325153448.0 | ||
| 008 | 200423s2019 hu o 0|| zxx d | ||
| 022 | |a 2064-8316 | ||
| 024 | 7 | |a 10.14232/actasm-018-538-y |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a zxx | ||
| 100 | 1 | |a Czédli Gábor | |
| 245 | 1 | 3 | |a On principal congruences and the number of congruences of a lattice with more ideals than filters |h [elektronikus dokumentum] / |c Czédli Gábor |
| 260 | |c 2019 | ||
| 300 | |a 363-380 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 85 No. 3-4 | |
| 520 | 3 | |a 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. | |
| 695 | |a Rácselmélet - rács szűrő - egyezések | ||
| 700 | 0 | 1 | |a Mureşan Claudia |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/66321/1/math_085_numb_003-004_363-380.pdf |z Dokumentum-elérés |