Some remarks on skew polynomial rings over reduced rings (Q2785275)

A ring \(R\) is called Baer if the right annihilator of every nonempty subset of \(R\) is generated, as a right ideal, by an idempotent of \(R\). For a reduced ring \(R\) and a monomorphism \(\alpha\) of \(R\) with \(\alpha(P)\subseteq P\) for any minimal prime ideal \(P\) of \(R\), it is shown that the skew polynomial ring \(R[x;\alpha]\) is Baer if and only if \(R\) is Baer.