The Growth of Varieties Generated by Upper-Triangular Matrices Algebras / *Ratseev S.M.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 1. P. 66-68
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 50-52].

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 order

*s*over an arbitrary field. V.M. Petrogradsky proved that the exponent of any subvariety of var(

*UT*) exists and is an integer number. In his paper the growth estimates for such varieties are reinforced.

_{s}
*Key words*:
algebra of upper triangular
matrices, growth, associative algebra.