Congruence lattices of free lattices in non-distributive varieties

Simple item page
dc.creatorPloscica, Miroslav
dc.creatorTuma, Jiri
dc.creatorWehrung, Friedrich
dc.date2005-01-25
dc.date.accessioned2026-07-07T05:16:24Z
dc.date.available2026-07-07T05:16:24Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/math/0501459
dc.identifierhttp://arxiv.org/abs/math/0501459
dc.identifierColloquium Mathematicum 76, no. 2 (1998) 269--278
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73975
dc.subjectGeneral Mathematics
dc.subjectPrimary 06B10, 06B15, 06B20, 06B25; Secondary 16E50, 08A05, 04A20
dc.titleCongruence lattices of free lattices in non-distributive varieties
dc.typetext

Files

Collections

arXiv