Geodesic
On the Nilindex of the Radical of a Relatively Free Associative Algebra
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 583-592

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In the paper, it is proved that the radical of a relatively free associative algebra of countable rank over an infinite field of characteristic $p>0$ is a nil ideal of bounded index if the complexity of the corresponding variety is less than $p$. Moreover, a description of a basis for trace identities for the matrix algebra $M_n$ over an infinite field of characteristic $p>0$, $n$, is obtained in the paper.
Keywords: nil ideal, relatively free associative algebra, nilindex, radical, trace identity, basis for trace identities, Cayley–Hamilton identity. 
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     author = {L. M. Samoilov},
     title = {On the {Nilindex} of the {Radical} of a {Relatively} {Free} {Associative} {Algebra}},
     journal = {Matemati\v{c}eskie zametki},
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     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a12/}
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L. M. Samoilov. On the Nilindex of the Radical of a Relatively Free Associative Algebra. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 583-592. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a12/