Geodesic
Radical of a relatively free associative algebra over fields of positive characteristic
Sbornik. Mathematics, Tome 199 (2008) no. 5, pp. 707-753 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The following Kemer problem on the nilindex of the radical is solved: it is shown that the Jacobson radical of a relatively free associative algebra over an infinite field of positive characteristic is a nilideal of bounded index. A basis of the identities with forms for matrix algebras over infinite fields of positive characteristic is described. Bibliography: 10 titles. 
@article{SM_2008_199_5_a4,
     author = {L. M. Samoilov},
     title = {Radical of a~relatively free associative algebra over fields of positive characteristic},
     journal = {Sbornik. Mathematics},
     pages = {707--753},
     year = {2008},
     volume = {199},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2008_199_5_a4/}
}
TY  - JOUR
AU  - L. M. Samoilov
TI  - Radical of a relatively free associative algebra over fields of positive characteristic
JO  - Sbornik. Mathematics
PY  - 2008
SP  - 707
EP  - 753
VL  - 199
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/SM_2008_199_5_a4/
LA  - en
ID  - SM_2008_199_5_a4
ER  - 
%0 Journal Article
%A L. M. Samoilov
%T Radical of a relatively free associative algebra over fields of positive characteristic
%J Sbornik. Mathematics
%D 2008
%P 707-753
%V 199
%N 5
%U http://geodesic.mathdoc.fr/item/SM_2008_199_5_a4/
%G en
%F SM_2008_199_5_a4
L. M. Samoilov. Radical of a relatively free associative algebra over fields of positive characteristic. Sbornik. Mathematics, Tome 199 (2008) no. 5, pp. 707-753. http://geodesic.mathdoc.fr/item/SM_2008_199_5_a4/

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

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

[3] L. M. Samoilov, “On the nilindex of the radical of a relatively free associative algebra”, Math. Notes, 82:3–4 (2007), 522–530 | DOI | MR

[4] A. R. Kemer, “Identities of finitely generated algebras over an infinite field”, Math. USSR-Izv., 37:1 (1991), 69–96 | DOI | MR | Zbl

[5] S. A. Amitsur, “On the characteristic polynomial of a sum of matrices”, Linear and Multilinear Algebra, 8:3 (1980), 177–182 | DOI | MR | Zbl

[6] C. Procesi, Rings with polynomial identities, Pure Appl. Math. (N.Y.), 17, Dekker, New York, 1973 | MR | Zbl

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

[8] A. N. Zubkov, “A generalization of the Razmyslov–Procesi theorem”, Algebra and Logic, 35:4 (1996), 241–254 | DOI | MR | Zbl

[9] S. Donkin, “Invariants of several matrices”, Invent. Math., 110:1 (1992), 389–401 | DOI | MR | Zbl

[10] C. Procesi, “The invariant theory of $n\times n$-matrices”, Advances in Math., 19:3 (1976), 306–381 | DOI | MR | Zbl