Congruence lattices of free lattices in non-distributive varieties
Miroslav Ploščica, Jiří Tůma, Friedrich Wehrung · Colloquium Mathematicum · 1998
We prove that for any free lattice F with at least ℵ 2 generators in any non-distributive variety of lattices, there exists no sectionally complemented lattice L with congruence lattice isomorphic to the one of F .This solves a question formulated by Grätzer and Schmidt in 1962.This in turn yields further examples of simply constructed distributive semilattices that are not isomorphic to the semilattice of finitely generated two-sided ideals in any von Neumann regular ring.