(σ,τ)-Derivations of group rings

Abstract

We study $(\sigma ,\tau )$-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 $\mathbb{Z}G$ to $(\sigma ,\tau )$-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 $(\sigma ,\tau )$-derivation case.