On the Group Ring

Let R be the discrete group ring of the group G over the ring A . In this paper we attempt to find necessary and sufficient conditions on G and A so that R will have some standard ring-theoretic property ; among the properties considered are those of being artinian, regular, self-injective, and semi-prime. The contents of this paper form essentially the author's doctoral thesis. The author would like to thank his supervisor Dr. J. Lambek for his generous encouragement and continued interest.