(σ,τ)-Derivations of group rings

Abstract

We study (σ,τ)-derivations of a group ring RG of a finite group G over an integral domain R with 1. As an application we extend a well known result on derivation of an integral group ring ZG to (σ,τ)-derivation on it for a finite group G with some conditions on σ and τ. In the process of the extension, a generalization of an application of Skolem-Noether Theorem to derivation on a finite dimensional central simple algebra has also been given for the (σ,τ)-derivation case.