A solution to Dilworth's Congruence Lattice Problem

Details A solution to Dilworth's Congruence Lattice Problem A solution to Dilworth's Congruence Lattice Problem

2006-01-04

arxiv.org/abs/math/0601059v5

Advances in Mathematics 216, 2 (2007) 610--625

Mathematics

Rings and Algebras

Version 1 presents a longer and slightly more general proof, based on so-called "uniform refinement properties". Version 2 pre

Scientific paper

10.1016/j.aim.2007.05.016

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.

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