Duo rings and the topological Baer radical
https://doi.org/10.22405/2226-8383-2026-27-2-150-155
Abstract
In the paper we prove that the topological Baer radical of a right bounded left duo ring coincides with its set of the all topologically nilpotent elements. After that we define topologically nil-Armendariz rings. We prove that every right bounded left duo ring is a topologically nil-Armendariz ring.
About the Authors
Damir Nailevich Belyalov
Lomonosov Moscow State University
Russian Federation
Russian Federation
Viktoria Vasilievna Tenzina
Lomonosov Moscow State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
References
1. Arnautov, V.I., Glavatsky, S.T. & Mikhalev, A.V. 1996, Introduction to the theory of topological rings and modules, Marcel Dekker, New York, 502 p.
2. Arnautov, V.I. 1964, “Topological Baer radical and decomposition of rings” [Topologicheskii radikal Bera i razlozhenie kolets], Sibirskii Matematicheskii Zhurnal, vol. 5, no. 6, pp. 1209– 1227.
3. Feller, E.H. 1958, “Properties of primary noncommutative rings”, Transactions of the American Mathematical Society, vol. 89, pp. 79–91.
4. Thierrin, G. 1960, “On duo rings”, Canadian Mathematical Bulletin, vol. 3, no. 2, pp. 167–172.
5. Rege, M. & Chhawchharia, S. 1997, “Armendariz rings”, Proceedings of the Japan Academy. Series A, Mathematical Sciences, vol. 73, pp. 14–17.
6. Antoine, R. 2008, “Nilpotent elements and Armendariz rings”, Journal of Algebra, vol. 319, pp. 3128–3140.
Review
For citations:
Belyalov D.N., Tenzina V.V. Duo rings and the topological Baer radical. Chebyshevskii Sbornik. 2026;27(2):150-155. (In Russ.) https://doi.org/10.22405/2226-8383-2026-27-2-150-155
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