Reversibility of skew Hurwitz series rings

Year 2020, Volume: 49 Issue: 6, 2074 - 2083, 08.12.2020

Fatma Kaynarca Muhammed Ali Yıldırım

https://doi.org/10.15672/hujms.679606

Cited By: 1

Abstract

We study the reversibility of skew Hurwitz series at zero as a generalization of an $\alpha$-rigid ring, introducing the concept of skew Hurwitz reversibility. A ring $R$ is called skew Hurwitz reversible ($SH$-reversible, for short), if the skew Hurwitz series ring $(HR,\alpha)$ is reversible i.e. whenever skew Hurwitz series $f, g\in (HR,\alpha)$ satisfy $fg=0$, then $gf=0$. We examine some characterizations and extensions of $SH$-reversible rings in relation with several ring theoretic properties which have roles in ring theory.

Keywords

Skew Hurwitz series ring, reversible ring, α-rigid ring, matrix ring

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