Skew Poincaré-Birkhoff-Witt extensions over weak $\Sigma$-rigid rings

Abstract

In this paper we introduce the notion of weak $\Sigma$-rigid ring which extends $\alpha$-rigid rings and $\Sigma$-rigid rings defined for Ore extensions and skew PBW extensions, respectively. We also present the notion of weak $\Sigma$-skew Armendariz ring which extends that of $\alpha$-skew Armendariz ring. In this way we generalize several results in the literature, from Ore extensions of injective type to the more general setting of skew PBW extensions.

12 pages. arXiv admin note: text overlap with arXiv:1612.06628, arXiv:1611.01562, arXiv:1805.11980