Reversible group rings

Abstract

AbstractThe problem we consider is when a group ring K[G] over a field is reversible, i.e. satisfies the implication (ab=0)→(ba=0). For G torsion-free, this is strictly connected with the zero divisor conjecture. In this paper, we characterize reversible rings K[G] for torsion groups. In particular, all finite reversible group rings are described. Our results exhibit a broad class of reversible rings, which are not symmetric