Geodesic
The intersection of the powers of the topological Jacobson radical and topological Krull dimension
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 243-252 
V. V. Tenzina. The intersection of the powers of the topological Jacobson radical and topological Krull dimension. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 243-252. http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, it is proved that a certain power of the topological Jacobson radical for a ring annihilates a left module having topological Krull dimension over this ring. The estimation of this power depends on the topological Krull dimension and the dual topological Krull dimension. A similar estimation for discrete Jacobson radical holds true. Levitzky's theorem is generalized for topological rings.

[1] Arnautov V. I., “K teorii topologicheskikh kolets”, DAN SSSR, 157:1 (1964) | Zbl

[2] Glavatskii S. T., Mikhalev A. V., Tenzina V. V., “Topologicheskii radikal Dzhekobsona kolets. I”, Fundament. i prikl. matem., 16:8 (2010), 49–68

[3] Glavatskii S. T., Mikhalev A. V., Tenzina V. V., “Topologicheskii radikal Dzhekobsona kolets. I”, Fundament. i prikl. matem., 17:1 (2011/2012), 53–64

[4] Tenzina V. V., “Topologicheskaya razmernost Krullya”, Fundament. i prikl. matem., 10:3 (2004), 215–230 | Zbl

[5] Tenzina V. V., “Nekotorye svoistva topologicheskogo radikala Bera kolets s topologicheskoi razmernostyu Krullya”, UMN, 60:2(362) (2005), 175–176 | DOI | MR | Zbl

[6] Jacobson N., “The radical and the semi-simplicity for arbitrary rings”, Amer. J. Math., 67 (1945), 300–320 | DOI | MR | Zbl

[7] Krause H., “On the nilpotency of the Jacobson radical for Noetherian rings”, Arch. Math., 70:6 (1998), 435–437 | DOI | MR | Zbl