Congruence lattices of free lattices in non-distributive varieties
Ploscica, Miroslav ; Tuma, Jiri ; Wehrung, Friedrich
HAL, hal-00004064 / Harvested from HAL
Text on HAL
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.
Publié le : 1998-07-05
Classification:  Kuratowski's Theorem,  diamond,  pentagon,  Congruence lattice,  congruence splitting lattice,  Uniform Refinement Property,  Primary 06B10, 06B15, 06B20, 06B25; Secondary 16E50, 08A05, 04A20,  [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] 
@article{hal-00004064,
     author = {Ploscica, Miroslav and Tuma, Jiri and Wehrung, Friedrich},
     title = {Congruence lattices of free lattices in non-distributive varieties},
     journal = {HAL},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00004064}
}

Ploscica, Miroslav; Tuma, Jiri; Wehrung, Friedrich. Congruence lattices of free lattices in non-distributive varieties. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-00004064/