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AAA60: Workshop on General Algebra (60. Arbeitstagung Allgemeine Algebra)
June 22-25, 2000
Dresden University of Technology
Dresden, Germany

Organizers
Reinhard Pöschel, Manfred Droste, Bernhard Ganter

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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:Conc K --> S, there are a lattice L, a lattice homomorphism f: K --> L, and an isomorphism \alpha:Conc L --> S such that j = \alpha o Concf;

(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

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-91.