No Associative PI-Algebra Coincides with Its Commutant

What is it about?

The main result of the paper is already stated in the title. This problem was posed by I. V. Lvov. First the author shows that it is enough to prove that no PI-algebra generating a $T$-prime variety coincides with its commutant. Then he derives the last fact from the following theorem: In every $T$-prime variety (of associative algebras) there is a weak identity, i.e., a polynomial that is not an identity of this variety but becomes such after substituting $[z,t]$ for one of its variables. The author also proves that every $T$-prime variety contains a central polynomial; is unitarily closed (in positive characteristic at the multilinear level) and is stable. Reviewed by Vladimir V. Shchigolev

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