A Note on Derivations of Group Rings

摘要

Let RG denote the group ring of a group G over a semiprime ring R. We prove that, if the center of G is of finite index and some natural restrictions hold, then every ^-derivation of RG is inner. We also give an example of a group G which is both locally finite and nilpotent and such that, for every field F, there exists an F-derivation of FG which is not inner.