Minimal representations of a finite distributive lattice by principal congruences of a lattice
Let the finite distributive lattice D be isomorphic to the congruence lattice of a finite lattice L. Let Q denote those elements of D that correspond to principal congruences under this isomorphism. Then Q contains 0, 1 ∈ D and all the join-irreducible elements of D. If Q contains exactly these elem...
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| Dokumentumtípus: | Cikk |
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2019
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| Sorozat: | Acta scientiarum mathematicarum
85 No. 1-2 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-017-060-9 |
| Online Access: | http://acta.bibl.u-szeged.hu/62134 |
| Tartalmi kivonat: | Let the finite distributive lattice D be isomorphic to the congruence lattice of a finite lattice L. Let Q denote those elements of D that correspond to principal congruences under this isomorphism. Then Q contains 0, 1 ∈ D and all the join-irreducible elements of D. If Q contains exactly these elements, we say that L is a minimal representation of D by principal congruences of the lattice L. We characterize finite distributive lattices D with a minimal representation by principal congruences with the property that D has at most two dual atoms. |
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| Terjedelem/Fizikai jellemzők: | 69-96 |
| ISSN: | 2064-8316 |