Paperback. " This useful book, which grew out of the author's lectures at Berkeley, presents some 400 exercises of varying degrees of difficulty in classical ring theory, together with complete solutions, background information, historical commentary, bibliographic details, and indications of possible improvements or generalizations. The book should be especially helpful to graduate students as a model of the problem-solving process and an illustration of the applications of different theorems in ring theory. The author also discusses "the folklore of the subject: the 'tricks of the trade' in ring theory, which are well known to the experts in the field but may not be familiar to others, and for which there is usually no good reference". The problems are from the following areas: the Wedderburn-Artin theory of semisimple rings, the Jacobson radical, representation theory of groups and algebras, (semi)prime rings, (semi)primitive rings, division rings, ordered rings, (semi)local rings, the theory of idempotents, and (semi)perfect rings. Problems in the areas of module theory, category theory, and rings of quotients are not included, since they will appear in a later book. " (T. W.Hungerford, Mathematical Reviews) The problems are from the following areas: the Wedderburn-Artin theory of semisimple rings, the Jacobson radical, representation theory of groups and algebras, (semi)prime rings, (semi)primitive rings, division rings, ordered rings, (semi)local rings, the theory of idempotents, and (semi)perfect rings. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Bibliographic Details

Title: Exercises in Classical Ring Theory (Paperback)
Publisher: Springer-Verlag New York Inc., New York, NY
Publication Date: 2010
Language: English
ISBN 10: 1441918299
ISBN 13: 9781441918291
Binding: Paperback
Condition: new

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The first work of its kind, this volume offers a compendium of 400 exercises of varying degrees of difficulty in classical ring theory. All exercises are solved in full detail; many are accompanied by historical or bibliographical information, or a commentary on possible improvements and generalizations. The second edition contains 40 new exercises with their solutions.

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