On $\Sigma$-skew reflexive-nilpotents-property for rings

TL;DR

This paper investigates the transfer of the $ abla$-skew reflexive-nilpotents-property in Ore and skew PBW extensions, introducing new ring classes and extending previous results in noncommutative ring theory.

Contribution

It introduces $ abla$-skew CN and RNP rings, and studies their transfer properties in Ore and skew PBW extensions under compatibility conditions.

Findings

Transfer of $ abla$-skew RNP property under certain conditions

Introduction of $ abla$-skew CN and RNP rings

Extension of previous results by Bhattacharjee

Abstract

In this paper, we study the reflexive-nilpotents-property (briefly, RNP) for Ore extensions of injective type, and more generally, skew PBW extensions. With this aim, we introduce the notions of $\Sigma$-skew CN rings and $\Sigma$-skew reflexive (RNP) rings, for $\Sigma$ a finite family of ring endomorphisms of a ring $R$. Under certain conditions of compatibility, we study the transfer of the $\Sigma$-skew RNP property from a ring of coefficients to an Ore extension or skew PBW extension over this ring. We also consider this property for localizations of these noncommutative rings. Our results extend those corresponding presented by Bhattacharjee \cite{Bhattacharjee2020}.