(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 1, PAGES 47-66

## On non-Spechtian varieties

A. Ya. Belov

Abstract

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This article is devoted to construction of infinitely based series of identities. Such counterexamples in Specht problem are built in any positive characteristics. The main result is the following:

\bfseries Theorem. Let $F$ be any field of characteristic $p$, $q=ps$, $s > 1$. Then the polynomials $R$n:

$R$n=[[E,T],T] Õ i=1nQ(xi,yi)([T,[T,F]][[E,T],T])q-1[T,[T,F]],

where $Q\left(x,y\right)=xp-1yp-1\left[x,y\right]$, generate an infinitely based variety.

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