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Journal of the American Mathematical Society

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The structure of locally finite varieties with polynomially many models

Authors: Paweł Idziak, Ralph McKenzie and Matthew Valeriote
Journal: J. Amer. Math. Soc. 22 (2009), 119-165
MSC (2000): Primary 08A05; Secondary 03C45
Published electronically: September 12, 2008
MathSciNet review: 2449056
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Abstract: 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

Ralph McKenzie
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240

Matthew Valeriote
Affiliation: Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1

Received by editor(s): June 26, 2006
Published electronically: September 12, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.