A solution to Dilworth's congruence lattice problem

• Autores: Friedrich Wehrung
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 216, Nº 2, 2007, págs. 610-625
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.05.016
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• Resumen

  • Abstract We construct an algebraic distributive 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 a compact top element and ?+1 compact elements. Our results extend to any algebra possessing a congruence-compatible structure of a join-semilattice with a largest element.