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A finite basis theorem for difference-term varieties with a finite residual bound


Authors: Keith Kearnes, Ágnes Szendrei and Ross Willard
Journal: Trans. Amer. Math. Soc. 368 (2016), 2115-2143
MSC (2010): Primary 03C05; Secondary 08B05
DOI: https://doi.org/10.1090/tran/6509
Published electronically: July 10, 2015
MathSciNet review: 3449235
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Abstract: We prove that if $ \mathcal V$ is a variety of algebras (i.e., an equationally axiomatizable class of algebraic structures) in a finite language, $ \mathcal V$ has a difference term, and $ \mathcal V$ has a finite residual bound, then $ \mathcal V$ is finitely axiomatizable. This provides a common generalization of R. McKenzie's finite basis theorem for congruence modular varieties with a finite residual bound, and R. Willard's finite basis theorem for congruence meet-semidistributive varieties with a finite residual bound.


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Additional Information

Keith Kearnes
Affiliation: Department of Mathematics, Campus Box 395, University of Colorado at Boulder, Boulder, Colorado 80309-0385

Ágnes Szendrei
Affiliation: Department of Mathematics, Campus Box 395, University of Colorado at Boulder, Boulder, Colorado 80309-0385 – and – Bolyai Institute, Aradi vértanúk tere 1, H-6720 Szeged, Hungary

Ross Willard
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

DOI: https://doi.org/10.1090/tran/6509
Received by editor(s): October 12, 2013
Received by editor(s) in revised form: June 3, 2014
Published electronically: July 10, 2015
Additional Notes: This material is based upon work supported by the Hungarian National Foundation for Scientific Research (OTKA) grants No. K83219 and K104251 and by the Natural Sciences and Engineering Research Council of Canada.
Article copyright: © Copyright 2015 American Mathematical Society

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