Armendariz modules over skew PBW extensions

Abstract

The aim of this article 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 these topics for the context of 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.

Keywords:

• Armendariz
• Baer
• quasi-Baer
• p.p. and p.q.-Baer rings
• skew PBW extensions

2010 Mathematics Subject Classification:

• 16S36
• 16T20
• 16E50
• 16S30

Acknowledgements

The author was supported by the research fund of Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá, Colombia, HERMES CODE 30366.

Disclosure statement

No potential conflict of interest was reported by the author.