Dover Books on Mathematics: The Algebraic Structure of Group Rings (Paperback)

"Highly recommended" by the Bulletin of the London Mathematical Society, this comprehensive, self-contained treatment of group rings was written by an authority on the subject. Suitable for graduate students, it was hailed by the Bulletin of the American Mathematical Society as "a majestic account… encyclopedic and lucid."
The three-part survey begins with an introduction that defines the trace map, considers the augmentation ideal in considerable detail, and provides all the necessary group ring results for later characterizations of dimension subgroups. A second section on linear identities characterizes prime and semiprime group rings, brings semisimplicity considerations into play, and offers construction techniques for obtaining primitive group rings. The final part, an exploration of finiteness properties, consists chiefly of a study of Noetherian group rings. Hundreds of exercises of varying difficulty appear throughout the text.