Representing a monotone map by principal lattice congruences
For a lattice L, let Princ (L) denote the ordered set of principal congruences of L. In a pioneering paper, G. Grätzer proved that bounded ordered sets (in other words, posets with 0 and 1) are, up to isomorphism, exactly the Princ (L) of bounded lattices L. Here we prove that for each 0-separating...
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| Dokumentumtípus: | Cikk |
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2015
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| Sorozat: | ACTA MATHEMATICA HUNGARICA
147 No. 1 |
| doi: | 10.1007/s10474-015-0539-0 |
| mtmt: | 2984003 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/14547 |
| Tartalmi kivonat: | For a lattice L, let Princ (L) denote the ordered set of principal congruences of L. In a pioneering paper, G. Grätzer proved that bounded ordered sets (in other words, posets with 0 and 1) are, up to isomorphism, exactly the Princ (L) of bounded lattices L. Here we prove that for each 0-separating boundpreserving monotone map ψ between two bounded ordered sets, there are a lattice L and a sublattice K of L such that, in essence, ψ is the map from Princ (K) to Princ (L) that sends a principal congruence to the congruence it generates in the larger lattice. © 2015, Akadémiai Kiadó, Budapest, Hungary. |
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| Terjedelem/Fizikai jellemzők: | 12-18 |
| ISSN: | 0236-5294 |