$(\sigma ,\tau )$-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 $\sigma$ and $\tau$. 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.