Congruence lattices of lattices with m-permutable congruences
We prove that there exists a lattice whose congruence lattice is not isomorphic to the congruence lattice of any lattice with m-permutable congruences. Our proof also extends to a wider class of algebras with m-permutable congruences. In order to do this we use and further develop the method invente...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2008
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| Sorozat: | Acta scientiarum mathematicarum
74 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16222 |
| Tartalmi kivonat: | We prove that there exists a lattice whose congruence lattice is not isomorphic to the congruence lattice of any lattice with m-permutable congruences. Our proof also extends to a wider class of algebras with m-permutable congruences. In order to do this we use and further develop the method invented by F. Wehrung for solving Dilworth's congruence lattice problem. To minimize the cardinality of our construction, we use the free trees combinatorial principle of P. Ruzicka. |
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| Terjedelem/Fizikai jellemzők: | 23-36 |
| ISSN: | 0001-6969 |