$\sigma$-PBW Extensions of Skew $\Pi$-Armendariz Rings

TL;DR

This paper introduces the concept of skew Pi-Armendariz rings within the framework of sigma-PBW extensions, generalizing existing Armendariz ring definitions for non-commutative rings and exploring their relationships with related ring properties.

Contribution

It defines skew Pi-Armendariz rings for sigma-PBW extensions and analyzes their connections with other ring properties, extending prior work on Armendariz rings in non-commutative algebra.

Findings

Generalization of Armendariz rings to sigma-PBW extensions

Establishment of relations between skew Pi-Armendariz and other ring properties

Extension of concepts to Ore extensions of injective type

Abstract

In this paper we present the notion of skew $\Pi$-Armendariz for the non-commutative rings known as $\sigma$-PBW extensions. This concept generalizes several definitions of Armendariz rings presented in the literature for these extensions, and in particular, for Ore extensions of injective type. We investigate the relations between skew $\Pi$-Armendariz, $\Sigma$-rigid, $(\Sigma,\Delta)$-skew Armendariz and $\Sigma$-skew Armendariz rings rings.