$$\Sigma$$-Semicommutative rings and their skew PBW extensions

Suárez, Héctor; Reyes, Armando

doi:10.1007/s40863-023-00356-w

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2024

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“…Since its introduction, ring-theoretical and homological properties of skew PBW extensions have been studied by some people (e.g. [5], [21], [22], [23], [44], [47], [70], [25], [56], [61], [66], [68], [69]). As a matter of fact, a book that includes several of the works carried out for these extensions has been published (Fajardo et al [16]).…”

Section: Introductionmentioning

confidence: 99%

On Σ-skew reflexive-nilpotents-property for rings

Suárez,

Higuera,

Reyes

2024

ADM

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In this paper, we study the reflexive-nilpotents-property (briefly, RNP) for skew PBW extensions. With this aim, we introduce the Σ-skew CN and Σ-skew reflexive (RNP) rings. Under conditions of compatibility, we investigate the transfer of there flexive-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].

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