Congruence lattices of free lattices in non-distributive varieties
General Mathematics
2007-05-23 v1
Abstract
We prove that for any free lattice F with at least 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 Gr\"{a}tzer 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.
Keywords
Cite
@article{arxiv.math/0501459,
title = {Congruence lattices of free lattices in non-distributive varieties},
author = {Miroslav Ploscica and Jiri Tuma and Friedrich Wehrung},
journal= {arXiv preprint arXiv:math/0501459},
year = {2007}
}