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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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Affine complete algebras in congruence permutable varieties
by
Erhard Aichinger
Johannes Kepler University Linz, Austria

Given a finite algebra A, we study the clone Comp (A) of all congruence preserving functions on A, and the clone Pol (A) of all polynomial functions on A. We call an algebra n-affine complete iff every n-ary congruence preserving function is polynomial.

We explain what results in universal algebra tell about the following questions:

  1. For k in N, which commutative rings with unity are k-affine complete?

  2. Is every 2-affine complete algebra n-affine complete for all n in N?

http://www.algebra.uni-linz.ac.at

Date received: February 12, 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-28.