FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 8, PAGES 49-68

The topological Jacobson radical of rings. I

S. T. Glavatsky
A. V. Mikhalev
V. V. Tenzina

Abstract

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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.

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