Geodesic
On nilpotency of graded associative algebras
Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 419-425 
A. D. Chanyshev. On nilpotency of graded associative algebras. Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 419-425. http://geodesic.mathdoc.fr/item/SM_1992_71_2_a9/
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     title = {On nilpotency of graded associative algebras},
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     url = {http://geodesic.mathdoc.fr/item/SM_1992_71_2_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that an associative PI-algebra over a field of characteristic zero that is graded by an arbitrary semigroup and that satisfies the relation $a^n=0$ for all homogeneous elements and is generated by a finite number of its homogeneous components is nilpotent. This generalizes a well-known theorem of M. Nagata.

[1] Nagata M., “On the nilpotency of nil algebras”, J. Math. Soc. Japan, 4 (1952), 296–301 | MR | Zbl

[2] Shirshov A. I., “O nekotorykh neassotsiativnykh nilkoltsakh i algebraicheskikh algebrakh”, Matem. sb., 41(83) (1957), 381–394 | Zbl

[3] Zelmanov E. I., “Ob engelevykh algebrakh Li”, Sib. matem. zhurn., 29:5 (1988), 112–117 | MR | Zbl

[4] Kostrikin A. I., Around Burnside, Springer-Verlag, 1989 | MR

[5] Thue A., “Über unendliche Zeichenreiken”, Norske Vid. Selsk. Skr., I Mat. Nat. Kl, 7, Christiania, 1906, 1–22

[6] Evdokimov A. A., “O silno asimmetrichnykh posledovatelnostyakh, porozhdennykh konechnym chislom simvolov”, DAN, 179:6 (1968), 1268–1271 | MR | Zbl