2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73975We prove that for any free lattice F with at least $\aleph\_2$ 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 yields in turn 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.General MathematicsPrimary 06B10, 06B15, 06B20, 06B25; Secondary 16E50, 08A05, 04A20text