On quasi-Baer rings of Ore extensions

TL;DR

This paper investigates the conditions under which the quasi-Baer property of a ring is preserved in its Ore extension, providing equivalence results and illustrative examples.

Contribution

It establishes necessary and sufficient conditions for a ring and its Ore extension to both be quasi-Baer, expanding understanding of ring extension properties.

Findings

R is quasi-Baer iff R[x;σ,δ] is quasi-Baer under certain conditions

Provides examples illustrating the main results

Delimits the scope of the equivalence with specific conditions

Abstract

Let $R$ be a ring and $S=R[x;\sigma,\delta]$ its Ore extension. We prove under some conditions that $R$ is a quasi-Baer ring if and only if the Ore extension $R[x;\sigma,\delta]$ is a quasi-Baer ring. Examples are provided to illustrate and delimit our results.