Representing homomorphisms of congruence lattices as restrictions of congruences of isoform lattices
Let L\ be a finite lattice with an ideal L2. Then the restriction map is a {0, l}-homomorphism from ConL\ into Conjoin 1986, the present authors published the converse. If D\ and D2 are finite distributive lattices, and <p : Di —> D2 is a {0, l}-homomorphism, then there are finite lattices L\...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2009
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| Sorozat: | Acta scientiarum mathematicarum
75 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16311 |
| Tartalmi kivonat: | Let L\ be a finite lattice with an ideal L2. Then the restriction map is a {0, l}-homomorphism from ConL\ into Conjoin 1986, the present authors published the converse. If D\ and D2 are finite distributive lattices, and <p : Di —> D2 is a {0, l}-homomorphism, then there are finite lattices L\ and L2 with an embedding 77 of L2 as an ideal of L\, and there are isomorphisms £1: ConLi —> D1 and e2'- Con L2 —• D2 such that ip is represented as the restriction map of congruences from Li to L2, up to the two isomorphisms. Let us call a lattice isoform, if for any congruence, all congruence classes are isomorphic lattices. In 2003, G. Gratzer and E. T. Schmidt proved that every finite distributive lattice can be represented as the congruence lattice of an isoform lattice. In this paper we combine the two results, reproving the 1986 result with isoform lattices. |
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| Terjedelem/Fizikai jellemzők: | 393-421 |
| ISSN: | 0001-6969 |