Geodesic
The topological Jacobson radical of rings. I
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 8, pp. 49-68 
S. T. Glavatsky; A. V. Mikhalev; V. V. Tenzina. The topological Jacobson radical of rings. I. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 8, pp. 49-68. http://geodesic.mathdoc.fr/item/FPM_2010_16_8_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, a topological Jacobson radical of rings is introduced. Several properties of this radical are considered. We investigate the topological Jacobson radical for some constructions of topological rings such as adjunction of the unitary element, completion, direct product with respect to the Tychonoff topology, rings of continuous functions, and polynomial rings.

[1] Arnautov V. I., “Topologicheskii radikal Bera i razlozhenie koltsa”, Sib. mat. zhurn., 5:6 (1964), 1209–1227 | MR | Zbl

[2] Arnautov V. I., “Obschaya teoriya radikalov topologicheskikh kolets”, Izv. AN RM, 1996, no. 2(21), 5–45 | MR | Zbl

[3] Arnautov V. I., Vodinchar M. I., “Radikaly topologicheskikh kolets”, Mat. issledovaniya, 3:2 (1968), 31–61 | MR | Zbl

[4] Arnautov V. I., Vodinchar M. I., Glavatskii S. T., Mikhalëv A. V., Konstruktsii topologicheskikh kolets, Shtiintsa, Kishinëv, 1988 | MR | Zbl

[5] Arnautov V. I., Mikhalëv A. V., “Topologii koltsa mnogochlenov i topologicheskii analog teoremy Gilberta o bazise”, Mat. sb., 116(158):4(12) (1981), 467–482 | MR | Zbl

[6] Ursul M. I., “Vedderbarnovskoe razlozhenie monokompaktnykh kolets”, Mat. issledovaniya, 1978, no. 48, 134–145 | MR | Zbl

[7] Arnautov V. I., Glavatsky S. T., Mikhalev A. V., Introduction to the Theory of Topological Rings and Modules, Marcel Dekker, New York, 1996 | MR | Zbl

[8] Kaplansky I., “Topological rings”, Amer. J. Math., 69 (1947), 153–183 | DOI | MR | Zbl

[9] Leptin H., “Linear kompakte Moduln und Ringe”, Math. Z., 62 (1955), 241–267 | DOI | MR | Zbl

[10] Weiss E., “Boundedness in topological rings”, Pacific J. Math., 6:1 (1956), 149–158 | DOI | MR | Zbl

[11] Yood B., “Closed prime ideals in topological rings”, Proc. London Math. Soc., 24 (1972), 307–323 | DOI | MR | Zbl