Reversibility Of Skew Hurwitz Series Rings

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 is an element of (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.