Reversibility of skew Hurwitz series rings

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.