FPM 1999, vol. 5, no. 1, pp. 47-66

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(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 $p$ , $q=p$ ^s, $s > 1$ . Then the polynomials $R$ _n:

R

_n=[[E,T],T] Õ _i=1ⁿQ(x_i,y_i)([T,[T,F]][[E,T],T])^q-1[T,[T,F]],

where $Q(x,y)=x$ ^p-1y^p-1[x,y], generate an infinitely based variety.

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