2005/01/25 by Miroslav Ploscica, Jiri Tuma, Friedrich Wehrung
Mathematics · #math.GM #msc:06B10 #msc:06B15 #msc:06B20 #msc:06B25 #msc:16E50 #msc:08A05 #msc:04A20
published as Colloquium Mathematicum 76, no. 2 (1998) 269--278
arxiv created 2005/01/25 · arxiv updated 2009/12/01
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 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.