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

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.