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The Regev conjecture and cocharacters for identities of associative algebras of PI-exponent 1 and 2

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Abstract

A result confirming the Regev conjecture for the codimension of associative algebras with unit which are of PI-exponent 2 is obtained. It is proved that the sequence of multiplicities of irreducible summands in proper cocharacters of algebras of PI-exponent 2 is of period 2, beginning with some index, whereas this sequence is constant for the ordinary cocharacters of the algebras of PI-exponent 1.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. S. Gordienko

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  1. A. S. Gordienko
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Correspondence to A. S. Gordienko.

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Original Russian Text © A. S. Gordienko, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 6, pp. 815–824.

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Gordienko, A.S. The Regev conjecture and cocharacters for identities of associative algebras of PI-exponent 1 and 2. Math Notes 83, 744–752 (2008). https://doi.org/10.1134/S0001434608050209

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  • DOI: https://doi.org/10.1134/S0001434608050209

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