The group ring K[G] is an associative ring which exhibits properties of the group G and the field of coefficients K. As the name implies, its study is a meeting place for group theory and ring theory, and as such it has been approached from many different points of view. For example, the finite group theorist does character theory and the analyst does operator theory and Fourier analysis. On the other hand, our approach here is purely algebraic and ring theoretic.