An independence theorem for ordered sets of principal congruences and automorphism groups of bounded lattices
For a bounded lattice L, the principal congruences of L form a bounded ordered set Princ(L). G. Gratzer proved in 2013 that every bounded ordered set can be represented in this way. Also, G. Birkhoff proved in 1946 that every group is isomorphic to the group of automorphisms of an appropriate lattic...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2016
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| Sorozat: | Acta scientiarum mathematicarum
82 No. 1-2 |
| Kulcsszavak: | Közelítés, Kongruencia rács probléma, rács automorfizmus, korlátos rács, rendezett halmaz, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-015-817-8 |
| Online Access: | http://acta.bibl.u-szeged.hu/40273 |
| Tartalmi kivonat: | For a bounded lattice L, the principal congruences of L form a bounded ordered set Princ(L). G. Gratzer proved in 2013 that every bounded ordered set can be represented in this way. Also, G. Birkhoff proved in 1946 that every group is isomorphic to the group of automorphisms of an appropriate lattice. Here, for an arbitrary bounded ordered set P with at least two elements and an arbitrary group G, we construct a selfdual lattice L of length sixteen such that Princ(L) is isomorphic to P and the automorphism group of L is isomorphic to G. |
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| Terjedelem/Fizikai jellemzők: | 3-18 |
| ISSN: | 0001-6969 |