Unsolvable one-dimensional lifting problems for congruence lattices of lattices
by
Jiri Tuma
Charles University, Prague
Coauthors: Friedrich Wehrung (Universite de Caen)

We prove the following result.

Theorem. Let S be a distributive {0, \/ }-semilattice. Then the following are equivalent:

(1) For any lattice K and any {0, \/ }-homomorphism j:Con_c K --> S, there are a lattice L, a lattice homomorphism f: K --> L, and an isomorphism \alpha:Con_c L --> S such that j = \alpha o Con_cf;

(2) S is a lattice.

The direction (ii) ===> (i) follows from an earlier paper by the second author.

http://www.math.unicaen.fr/~wehrung

Date received: June 6, 2000