Geodesic
The growth of varieties generated by upper-triangular matrices algebras
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2011), pp. 66-68

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It is shown that if the characteristic of the basic field does not equal two, then there exists no variety of associative algebras whose growth is intermediate between polynomial and exponential. Let $UT_s$ be the algebra of upper triangular matrices of dimension $s$ over an arbitrary field. V. M. Petrogradsky proved that the exponent of any subvariety of $\operatorname{var}(UTs)$ exists and is an integer number. In his paper the growth estimates for such varieties are strengthened. 
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     author = {S. M. Ratseev},
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S. M. Ratseev. The growth of varieties generated by upper-triangular matrices algebras. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2011), pp. 66-68. http://geodesic.mathdoc.fr/item/VMUMM_2011_1_a13/