Geodesic
The structure of locally finite varieties with polynomially many models
Idziak, Paweł1 ; McKenzie, Ralph2 ; Valeriote, Matthew3
1 Department of Theoretical Computer Science, Jagiellonian University, Kraków, Poland
2 Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
3 Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Journal of the American Mathematical Society, Tome 22 (2009) no. 1, pp. 119-165

Voir la notice de l'article provenant de la source American Mathematical Society

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 $H$.
DOI : 10.1090/S0894-0347-08-00614-0

Idziak, Paweł 1 ; McKenzie, Ralph 2 ; Valeriote, Matthew 3

1 Department of Theoretical Computer Science, Jagiellonian University, Kraków, Poland
2 Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
3 Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1 
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Idziak, Paweł; McKenzie, Ralph; Valeriote, Matthew. The structure of locally finite varieties with polynomially many models. Journal of the American Mathematical Society, Tome 22 (2009) no. 1, pp. 119-165. doi: 10.1090/S0894-0347-08-00614-0

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