Noncommutative Rings

1. Front Matter

   Pages i-ix

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2. The Representation Theory of Noetherian Rings

   • Kenneth A. Brown

   Pages 1-25

3. Some Ring Theoretic Techniques and Open Problems in Enveloping Algebras

   • Anthony Joseph

   Pages 27-67

4. Crossed Products: Characters, Cyclic Homology, and Grothendieck Groups

   • Martin Lorenz

   Pages 69-98

5. Prime Ideals in Crossed Products

   • D. S. Passman

   Pages 99-113

6. Category Theory and Quantum Field Theory

   • Marc A. Rieffel

   Pages 115-129

7. Quantum Groups: An Introduction and Survey for Ring Theorists

   • S. P. Smith

   Pages 131-178

This volume collects some of the survey lectures delivered at the Micro­ program on Noncommutative Rings held at MSRI, July 10-21, 1989. While the program was concerned with recent advances in ring theory, it also had as an important component lectures on related areas of mathematics where ring theory might be expected to have an impact. Thus, there are lectures of S. P. Smith on quantum groups and Marc Ri­ effel on algebraic aspects of quantum field theory. Martin Lorenz and Don­ ald Passman consider in their lectures various aspects of crossed products: homological and K-theoretic to group actions. Kenneth Brown presents the "modern" theory of Noetherian rings and localization. These contributions as well as the others not presented here show that ring theory remains a vigorous and useful area. The planning and organization of the program were done by the under­ signed and the late Robert Warfield. His illness prevented his attendance at the meeting. It is to him we dedicate this volume. The organizers wish to extend their thanks to Irving Kaplansky, Director of MSRI, and the staff for all of their efforts in making this conference such a success. Susan Montgomery Lance Small vii NONCOMMUTATIVE RINGS TABLE OF CONTENTS PREFACE. . . . . . . . . . . . . . . . . . . . . . .. . . . Vll . . . . . . . . . . K. A. Brown THE REPRESENTATION THEORY OF NOETHERIAN RINGS 1 A. Joseph SOME RING THEORETIC TECHNIQUES AND OPEN PROBLEMS IN ENVELOPING ALGEBRAS. . . . . . . . . . . 27 . . . M. Lorenz CROSSED PRODUCTS: CHARACTERS, CYCLIC HOMOLOGY, AND GROTHENDIECK GROUPS . . . . . . . . . . . . . . . 69 . . . . . .

• Category theory
• algebra
• commutative ring
• representation theory
• ring theory

• Department of Mathematics, University of Southern California, Los Angeles, USA

  Susan Montgomery

• Department of Mathematics, University of California at San Diego, La Jolla, USA

  Lance Small

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