Ring Theory (Pure and applied mathematics, vol.44) - Hardcover

Inhaltsangabe

The first five chapters of this book give an introduction to the theory of rings (the Jacobson density theorem, semisimple artinian rings, completely reducible modules, and representation theory). chapters VI-XI are devoted to various aspects of the theory of associative rings with radical different from zero, and the last chapter (Chapter XII) deals with rings of continuous functions, culminating with the theorems of Arens-Kaplansky and of Stone. Except for some minor changes and corrections, the first part of the book is a direct translation of the author's "Algebren," Mannheim, 1965. The author is indebted to Dr. E. Hotzel for pointing out some errors in the German edition. In the second half of the book, semiperfect rings plag the most important role, particularly in the chapter dealing with distributively representable rings. The section an arithmetic rings which forms part of this chapter contains a number of hitherto unpublished results. In Order to give the broadest possible view of ring theory compatible with keeping the book to a reasonable size, 1 haue had to omit a number of important topics, among them division rings—a treatment of which will be found in Jacobson's "Structure of Rings"—and the application of homological methods to ring theory. However, projective and injective modules are introduced in Chapter VII and the results obtained are applied to the theory of Asano ordern and seif-injective rings. Once again, I would like to express my appreciation to the "Bibliographisches Institut" in Mannheim. I would also like to thank Academic Press for undertaking to publish the book and for their patience in the face of mang delays. Finally, my sincere thanks go to Professor Clive Reis of the University of Western Ontario for translating the German manuscript.

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