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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. 66, No 1, 2011. 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 UTs 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(UTs) exists and is an integer number. In his paper the growth estimates for such varieties are reinforced.
Key words: algebra of upper triangular
matrices, growth, associative algebra.
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