Subexponential Estimations in the Shirshov Height Theorem

What is it about?

Applications of Shirshov's height theorem are considered in this article. First, a review of previous results is given. Then the authors offer a heretofore unexpected subexponential estimation of the nilpotency index of an associative algebra that depends on its nil-degree and quantity of generators. The suggested result is true in arbitrary characteristic. The work is based on word and graph combinatorics. Reviewed by Andrew Borisovich Verëvkin

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