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Let $R$ be a ring and $\sigma$ an endomorphism of $R$. In this note, we studyskew polynomial rings and skew power series rings over idempotent reflexiverings 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 areobtained as corollaries from our results.

Skew polynomial rings over abelian and idempotent reflexive rings