FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 2, PAGES 111-118

On $$S-nilpotent ideals of topological PI-rings

V. T. Markov
V. V. Tenzina

Abstract

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We show that under certain conditions on the topology of a faithful module $M$ over a topological PI-ring $R$, if $M$ has at most countable dual topological Krull dimension, then the closure of the sum of all $$S-nilpotent ideals of the ring $R$ is a $$S-nilpotent ideal too, and in the case of a bounded ring $R$ its topological Baer radical is $$S-nilpotent.

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Last modified: June 17, 2006