arXiv math/05014592005-01-25math.GM

Congruence lattices of free lattices in non-distributive varieties

Miroslav Ploscica, Jiri Tuma, Friedrich Wehrung

发表信息：: Colloquium Mathematicum 76, no. 2 (1998) 269--278

英文摘要：

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 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.

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