Ore extensions of principally quasi-Baer rings

Abstract

Let $R$ be a ring and $(\sigma,\delta)$ a quasi-derivation of $R$. In this paper, we show that if $R$ is an $(\sigma,\delta)$-skew Armendariz ring and satisfies the condition $(\mathcal{C_{\sigma}})$, then $R$ is right p.q.-Baer if and only if the Ore extension $R[x;\sigma,\delta]$ is right p.q.-Baer. As a consequence we obtain a generalization of \cite{hong/2000}.