Mathematics – General Mathematics
Scientific paper
2005-01-25
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.
Ploscica Miroslav
Tuma Jiri
Wehrung Friedrich
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