Bootstrapping the bounded nilradical. (Q387395)

Let \(R\) be a ring. In this paper the author defines and studies the set \(B(R)=\{a\in R:aR\) is nil of bounded index\} which is called the bounded nilradical of \(R\). The author gives some characterizations of \(B(R)\), that are too technical to be included in this review. The author shows that \(B(\mathbb M_n(R))=\mathbb M_n(B(R))\) for any ring \(R\) and if \(R\) is a \(\mathbb Z\)-graded ring, then \(B(R)\) is a \(\mathbb Z\)-graded ideal. Moreover, the author describes the bounded nilradical of skew polynomial and skew Laurent polynomial rings in terms of their coefficient rings.