Skew polynomial rings over abelian and idempotent reflexive rings

TL;DR

This paper investigates skew polynomial and power series rings over specific classes of rings, introducing new concepts like right and left $\sigma$-idempotent reflexive rings to generalize existing ring properties.

Contribution

It introduces the concept of right and left $\sigma$-idempotent reflexive rings, extending the theory of idempotent reflexive and $\sigma$-abelian rings in the context of skew polynomial rings.

Findings

Characterization of skew polynomial rings over abelian rings

Introduction of $\sigma$-idempotent reflexive rings and their properties

Derivation of corollaries from main results

Abstract

Let $R$ be a ring and $\sigma$ an endomorphism of $R$. In this note, we study skew polynomial rings and skew power series rings over idempotent reflexive rings and abelian rings. Also, we introduce the concept of right (resp., left) $\sigma$-idempotent reflexive rings which generalizes right (resp., left) idempotent reflexive rings and $\sigma$-abelian rings. Certain results are obtained as corollaries from our results.