A topological prime quasiradical
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 3, pp. 11-22
Citer cet article
Voir la notice de l'article provenant de la source Math-Net.Ru
In this paper, we consider a topological prime quasi-radical $\mu(R)$, which is the intersection of closed prime ideals in a topological ring $R$. Examples are given that show that $\mu(R)$ is different from those topological analogs of the prime radical that have been studied earlier. The topological prime quasi-radicals of matrix rings and rings of polynomials are investigated.
[1] Andrunakievich V. A., Ryabukhin Yu. M., Radikaly algebry i strukturnaya teoriya, Nauka, M., 1979 | MR
[2] Arnautov V. I., “Topologicheskii radikal Bera i razlozhenie kolets”, Sib. matem. zhurn., 5:6 (1964), 1209–1227 | MR | Zbl
[3] Arnautov V. I., “Obschaya teoriya radikalov topologicheskikh kolets”, Izv. AN RM. Mat., 2(21) (1996), 5–45 | MR | Zbl
[4] Burbaki N., Obschaya topologiya, IL, M., 1969
[5] 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