On \(\Sigma\)-skew reflexive-nilpotents-property for rings

Abstract

In this paper, we study the reflexive-nilpotents-property (briefly, RNP) for skew PBW extensions. With this aim, we introduce the \(\Sigma\)-skew CN and \(\Sigma\)-skew reflexive (RNP) rings. Under conditions of compatibility, we investigate the transfer of the reflexive-nilpotents-property from a ring of coefficients to a skew PBW extension. We also consider this property for localizations on these families of noncommutative rings. Our results extend those corresponding presented by Bhattacharjee [9].