Congruence lattices of free lattices in non-distributive varieties

Details Congruence lattices of free lattices in non-distributive varieties Congruence lattices of free lattices in non-distributive varieties

2005-01-25

arxiv.org/abs/math/0501459v1

Colloquium Mathematicum 76, no. 2 (1998) 269--278

Mathematics

General Mathematics

Scientific paper

We 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 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.

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