On Σ-nilpotent ideals of topological PI-rings

Abstract

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 Σ-nilpotent ideals of the ring R is a Σ-nilpotent ideal too, and in the case of a bounded ring R its topological Baer radical is Σ-nilpotent.