Congruence lattices of free lattices in non-distributive varieties

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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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General Mathematics, Primary 06B10, 06B15, 06B20, 06B25; Secondary 16E50, 08A05, 04A20

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http://salesiana.dossiersoluciones.com/handle/123456789/73975

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501459
 http://arxiv.org/abs/math/0501459
 Colloquium Mathematicum 76, no. 2 (1998) 269--278

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arXiv