A solution to Dilworth's Congruence Lattice Problem
| dc.creator | Wehrung, Friedrich | |
| dc.date | 2006-01-04 | |
| dc.date | 2007-11-10 | |
| dc.date.accessioned | 2026-07-07T08:41:41Z | |
| dc.date.available | 2026-07-07T08:41:41Z | |
| dc.description | We construct a distributive algebraic lattice D that is not isomorphic to the congruence lattice of any lattice. This solves a long-standing open problem, traditionally attributed to R. P. Dilworth, from the forties. The lattice D has compact top element and aleph omega+1 compact elements. Our results extend to all algebras possessing a polynomially definable structure of a join-semilattice with a largest element. | |
| dc.description | Version 1 presents a longer and slightly more general proof, based on so-called "uniform refinement properties". Version 2 presents a shorter proof. Versions 3 an 4 add a few minor improvements. Version 5 fixes a minor oversight in the proof of Theorem 7.1 | |
| dc.identifier | https://arxiv.org/abs/math/0601059 | |
| dc.identifier | http://arxiv.org/abs/math/0601059 | |
| dc.identifier | Advances in Mathematics 216, 2 (2007) 610--625 | |
| dc.identifier | doi:10.1016/j.aim.2007.05.016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141750 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 06B15, 06B10, 06A12. Secondary 08A30, 08B10, 16E50, 19A49 | |
| dc.title | A solution to Dilworth's Congruence Lattice Problem | |
| dc.type | text |