On a theorem of Kemer (Q1068168)

\textit{A. R. Kemer} has shown that every (associative, characteristic zero) algebra which satisfies a standard identity \(S_ n\) must also satisfy some Capelli identity \(d_ m\) [see Mat. Zametki 23, 753-757 (1978; Zbl 0436.16013)]. In this paper the author proves the following result: if \(m=the\) least integer \(\geq \log_ 2(3n-1)\), \(k(n)=the\) last integer such that \(d_{k(n)}\) is a consequence of \(S_ n\), then \(k(n)\leq ([n/2]^ 2+1)^ m.\) Remark. \(''m\geq \log_ 2(2n-1)''\) should be \(''m\geq \log_ 2(3n-1)''\) in the theorem of this paper.