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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A finite basis theorem for difference-term varieties with a finite residual bound
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by Keith Kearnes, Ágnes Szendrei and Ross Willard PDF
Trans. Amer. Math. Soc. 368 (2016), 2115-2143 Request permission

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
  • MR Author ID: 99640
  • 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
  • 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.
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 2115-2143
  • MSC (2010): Primary 03C05; Secondary 08B05
  • DOI: https://doi.org/10.1090/tran/6509
  • MathSciNet review: 3449235