The Algebraic Structure of Group Rings

The Algebraic Structure of Group Rings

Paperback Dover Books on Mathematics

By (author) Donald S. Passman

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  • Publisher: Dover Publications Inc.
  • Format: Paperback | 752 pages
  • Dimensions: 154mm x 234mm x 44mm | 975g
  • Publication date: 25 November 2011
  • Publication City/Country: New York
  • ISBN 10: 0486482065
  • ISBN 13: 9780486482064
  • Edition statement: Reprint
  • Sales rank: 1,294,239

Product description

"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.

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Table of contents

Part 1 Introduction1. Group Rings2. The Trace Map3. The Augmentation IdealPart 2 Linear Identities4. The Center5. Polynomial Identities6. Bounded Representation Degree7. The Semisimplicity Problem8. The Nilpotent Radical9. Primitive RingsPart 3 Finiteness Properties10. Chain Conditions11. Nilpotent Groups12. Finite Dimensional Modules13. The Zero Divisor Problem14. Isomorphism QuestionsReferencesIndexAppendix