$\sigma$-PBW Extensions of Skew Armendariz Rings

TL;DR

This paper explores $\sigma$-PBW extensions over Armendariz rings, establishing properties like Baer and p.q.-Baer, and generalizing results from Ore and skew PBW extensions.

Contribution

It introduces a general framework for $\sigma$-PBW extensions over Armendariz rings and extends known properties to this broader context.

Findings

$\sigma$-PBW extensions are Baer, quasi-Baer, p.p., and p.q.-Baer.

Generalizes results from Ore extensions of injective type.

Provides new insights into the structure of skew PBW extensions.

Abstract

The aim of this paper is to investigate a general notion of $\sigma$-PBW extensions over Armendariz rings. As an application, the properties of being Baer, quasi-Baer, p.p. and p.q.-Baer are established for these extensions. We generalize several results in the literature for Ore extensions of injective type and skew PBW extensions.