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The structure of locally finite varieties with polynomially many models
Author(s):
Paweł
Idziak;
Ralph
McKenzie;
Matthew
Valeriote
Journal:
J. Amer. Math. Soc.
22
(2009),
119-165.
MSC (2000):
Primary 08A05;
Secondary 03C45
Posted:
September 12, 2008
MathSciNet review:
2449056
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Abstract:
We prove that a locally finite variety has at most polynomially many (in  ) non-isomorphic  -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  -sets, with constants, for various finite groups  .
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Additional Information:
Paweł
Idziak
Affiliation:
Department of Theoretical Computer Science, Jagiellonian University, Kraków, Poland
Email:
idziak@tcs.uj.edu.pl
Ralph
McKenzie
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email:
ralph.n.mckenzie@vanderbilt.edu
Matthew
Valeriote
Affiliation:
Department of Mathematics \& Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Email:
matt@math.mcmaster.ca
DOI:
10.1090/S0894-0347-08-00614-0
PII:
S 0894-0347(08)00614-0
Received by editor(s):
June 26, 2006
Posted:
September 12, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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