(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.

Keywords:

• Derivations
• group rings

2010 Mathematics Subject Classification:

• 16S34
• 16W25

Acknowledgements

The author is thankful to DAE (Government of India) and National Board for Higher Mathematics for providing fellowship with reference number $2/40(16)/2016/$ R&D-II/5766. The author would also like to thank IISER Mohali for providing good research facilities when this project was carried out.