Armendariz Modules over Skew PBW Extensions
Armando Reyes
TL;DR
This paper develops the theory of skew Armendariz and quasi-Armendariz modules over skew PBW extensions, generalizing and unifying various properties from Ore extensions to broader non-commutative rings.
Contribution
It introduces a generalized framework for skew Armendariz modules over skew PBW extensions, extending existing results to non-iterated Ore-like rings.
Findings
Unified results on Armendariz, Baer, p.p., and p.q.-Baer properties
Extended theory to non-commutative rings beyond Ore extensions
Generalized properties for skew PBW extensions
Abstract
The aim of this paper is to develop the theory of skew Armendariz and quasi-Armendariz modules over skew PBW extensions. We generalize the results of several works in the literature concerning Ore extensions to another non-commutative rings which can not be expressed as iterated Ore extensions. As a consequence of our treatment, we extend and unify different results about the Armendariz, Baer, p.p., and p.q.-Baer properties for Ore extensions and skew PBW extensions.
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