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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Constantive Mal'cev clones on finite sets are finitely related


Author: Erhard Aichinger
Journal: Proc. Amer. Math. Soc. 138 (2010), 3501-3507
MSC (2010): Primary 08A40
Published electronically: May 14, 2010
MathSciNet review: 2661550
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Abstract: We show that on a finite set there are at most countably many constantive clones that contain a Mal'cev operation, and each such clone can be described by a single finitary relation. Thus, modulo polynomial equivalence and renaming of the elements, there are only countably many finite algebras that contain a Mal'cev term.


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Additional Information

Erhard Aichinger
Affiliation: Institut für Algebra, Johannes Kepler Universität Linz, Altenbergerstraße 69, 4040 Linz, Austria
Email: erhard@algebra.uni-linz.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10395-7
PII: S 0002-9939(2010)10395-7
Received by editor(s): August 24, 2009
Received by editor(s) in revised form: January 19, 2010
Published electronically: May 14, 2010
Communicated by: Julia Knight
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.