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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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/

[1] A. R. Kemer, “PI-algebras and nil algebras of bounded index”, Trends in ring theory (Miskolc, 1996), CMS Conf. Proc., 22, Amer. Math. Soc., Providence, RI, 1998, 59–69 | MR | Zbl

[2] P. Koshlukov, “Basis of the identities of the matrix algebra of order two over a field of characteristic $p\ne2$”, J. Algebra, 241:1 (2001), 410–434 | DOI | MR | Zbl

[3] A. R. Kemer, Ideal of Identities of Associative Algebras, Translations of Mathematical Monographs, 87, Amer. Math. Soc., Providence, RI, 1991 | MR | Zbl

[4] I. Yu. Sviridova, “Varieties and algebraic algebras of bounded degree”, J. Pure Appl. Algebra, 133:1–2 (1998), 233–240 | DOI | MR | Zbl

[5] Yu. P. Razmyslov, “Tozhdestva so sledom polnoi matrichnoi algebry nad polem kharakteristiki nul”, Izv. AN SSSR. Ser. matem., 38:4 (1974), 723–756 | MR | Zbl

[6] A. R. Kemer, “Multilinear identities of the algebras over a field of characteristic $p$”, Internat. J. Algebra Comput., 5:2 (1995), 189–197 | DOI | MR | Zbl

[7] C. Procesi, Rings with Polynomial Identities, Pure and Applied Mathematics, 17, Marcel Dekker, Inc., New York, 1973 | MR | Zbl