a module "m" over "r"["g"] is then the same as a linear representation of "g" over the field "r". there is no particular reason to limit "r" to be a field here. however, the classical results were obtained first when "r" is the complex number field and "g" is a finite group, so this case deserves close attention. it was shown that "r"["g"] is a semisimple ring, under those conditions, with profound implications for the representations of finite groups. more generally, whenever the characteristic of the field "r" does not divide the order of the finite group "g", then "r"["g"] is semisimple (maschke's theorem).