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Fundam. Prikl. Mat., 1999, Volume 5, Issue 1, Pages 47–66 (Mi fpm365)  

This article is cited in 29 scientific papers (total in 29 papers)

On non-Spechtian varieties

A. Ya. Belov

House of scientific and technical work of youth

Abstract: 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:
Theorem. Let $F$ be any field of characteristic $p$, $q=p^s$, $s>1$. Then the polynomials $R_n$:
$$ R_n=[[E,T],T]\prod_{i=1}^n Q(x_i,y_i) ([T,[T,F]][[E,T],T])^{q-1}[T,[T,F]], $$
where $Q(x,y)=x^{p-1}y^{p-1}[x,y]$, generate an infinitely based variety.

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Bibliographic databases:
UDC: 512.55
Received: 01.11.1998

Citation: A. Ya. Belov, “On non-Spechtian varieties”, Fundam. Prikl. Mat., 5:1 (1999), 47–66

Citation in format AMSBIB
\by A.~Ya.~Belov
\paper On non-Spechtian varieties
\jour Fundam. Prikl. Mat.
\yr 1999
\vol 5
\issue 1
\pages 47--66

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    This publication is cited in the following articles:
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    2. Giambruno, A, “On the identities of the Grassmann algebras in characteristic p > 0”, Israel Journal of Mathematics, 122 (2001), 305  crossref  mathscinet  zmath  isi
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    5. A. Ya. Belov, “No associative $PI$-algebra coincides with its commutant”, Siberian Math. J., 44:6 (2003), 969–980  mathnet  crossref  mathscinet  zmath  isi  elib
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