On Commutativity of Skew Polynomials at Zero

We, in this paper, study the commutativity of skew polynomials at zero as a generalization of an <TEX>α-rigid</TEX> ring, introducing the concept of strongly skew reversibility. A ring R is be said to be strongly <TEX>α-skew</TEX> reversible if the skew polynomial ring <TEX>R[x;α]</TEX> is reversible. We examine some characterizations and extensions of strongly <TEX>α-skew</TEX> reversible rings in relation with several ring theoretic properties which have roles in ring theory.