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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.
Ian G. Connell (Tue,) studied this question.