Ore extensions of principally quasi-Baer rings

TL;DR

This paper investigates the conditions under which Ore extensions of rings preserve the property of being right principally quasi-Baer, extending previous results in ring theory.

Contribution

It establishes an equivalence between the right p.q.-Baer property of a ring and its Ore extension under specific conditions, generalizing earlier work.

Findings

Ore extension preserves right p.q.-Baer property under certain conditions

Rings satisfying ( ext{C}_\sigma) and being ( ext{ extsigma}, ext{ extdelta})-skew Armendariz are characterized

Generalizes previous results on ring extensions and p.q.-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}.