Geodesic
Regev's and Amitsur's conjectures for codimensions of generalized polynomial identities
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 53-62 
A. S. Gordienko. Regev's and Amitsur's conjectures for codimensions of generalized polynomial identities. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 53-62. http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a5/
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     author = {A. S. Gordienko},
     title = {Regev's and {Amitsur's} conjectures for codimensions of generalized polynomial identities},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {53--62},
     year = {2008},
     volume = {14},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $A$ be a finite-dimensional associative algebra over a field of characteristic 0. Then there exist $C\in\mathbb Q_+$ and $t\in\mathbb Z_+$ such that $\mathrm{gc}_n(A)\sim Cn^td^n$ as $n\to\infty$, where $d=\mathrm{PI}\exp(A)$. In particular, Amitsur's and Regev's conjectures hold for the codimensions $\mathrm{gc}_n(A)$ of generalized polynomial identities.

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