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AAA63-Workshop on General Algebra (63. Arbeitstagung Allgemeine Algebra) combined with CYA17-Conference of Young Algebraists (17. Tagung junger Algebraiker)
February 22-24, 2002
University of Kaiserslautern, Department of Mathematics
Kaiserslautern, Germany

Organizers
Dietmar Schweigert

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On the tolerance lattices of algebras in congruence distributive varieties
by
Sándor Radeleczki
University of Miskolc, Institute of Mathematics, Hungary
Coauthors: G. Czédli (University of Szeged, Hungary), E.K. Horváth (University of Szeged, Hungary)

The first part of the lecture contains some joint results of G. Czédli, K. E. Horváth, and S. Radeleczki. They proved that the tolerance lattice Tol(A) of an algebra A from a congruence modular variety V is 0-1 modular and satisfies the general disjointness property. If V is congruence distributive, then the lattice Tol(A) is pseudocomplemented. If V admits a majority term, then Tol(A) is 0-modular. In addition, generalizing a result of D. Schweigert and S. Radeleczki, the author establish a structure theorem for congruence distributive algebras with a Boolean tolerance lattice.

Date received: February 6, 2002

Copyright © 2002 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 # caht-18.