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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The structure of locally finite varieties with polynomially many models
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by Paweł Idziak, Ralph McKenzie and Matthew Valeriote PDF
J. Amer. Math. Soc. 22 (2009), 119-165 Request permission


We prove that a locally finite variety has at most polynomially many (in $k$) non-isomorphic $k$–generated algebras if and only if it decomposes into a varietal product of an affine variety over a ring of finite representation type, and a sequence of strongly Abelian varieties equivalent to matrix powers of varieties of $H$-sets, with constants, for various finite groups $H$.
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Additional Information
  • Paweł Idziak
  • Affiliation: Department of Theoretical Computer Science, Jagiellonian University, Kraków, Poland
  • Email:
  • Ralph McKenzie
  • Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
  • Email:
  • Matthew Valeriote
  • Affiliation: Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
  • Email:
  • Received by editor(s): June 26, 2006
  • Published electronically: September 12, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 22 (2009), 119-165
  • MSC (2000): Primary 08A05; Secondary 03C45
  • DOI:
  • MathSciNet review: 2449056