Lattices embeddable in three-generated lattices
We prove that every finite lattice L can be embedded in a threegenerated finite lattice K. We also prove that every algebraic lattice with accessible cardinality is a complete sublattice of an appropriate algebraic lattice K such that K is completely generated by three elements. Note that ZFC has a...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2016
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| Sorozat: | Acta scientiarum mathematicarum
82 No. 3-4 |
| Kulcsszavak: | Rácsok, Schmidt Tamás, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-015-586-2 |
| Online Access: | http://acta.bibl.u-szeged.hu/46316 |
| Tartalmi kivonat: | We prove that every finite lattice L can be embedded in a threegenerated finite lattice K. We also prove that every algebraic lattice with accessible cardinality is a complete sublattice of an appropriate algebraic lattice K such that K is completely generated by three elements. Note that ZFC has a model in which all cardinal numbers are accessible. Our results strengthen P. Crawley and R. A. Dean's 1959 results by adding finiteness, algebraicity, and completeness. |
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| Terjedelem/Fizikai jellemzők: | 361-382 |
| ISBN: | 0001-6969 |