Exercises in Classical Ring Theory

T. Y. Lam

ISBN 10: 1441918299 / ISBN 13: 9781441918291

Editore: Springer New York, Springer US Nov 2010, 2010

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Neuware -' 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)Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 384 pp. Englisch.

Codice articolo 9781441918291

Dati bibliografici

• Titolo: Exercises in Classical Ring Theory
• Editore: Springer New York, Springer US Nov 2010
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 1441918299
• ISBN 13: 9781441918291
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 21 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 21 millimetri di profondità
• Peso: 581 grammi

Descrizione articolo

Riassunto

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.

Contenuti

* Preface * Notes to the Reader * Wedderburn-Artin Theory * Jacobson Radical Theory * Introduction to Representation Theory * Prime and Primitive Rings * Introduction to Division Rings * Ordered Structures in Rings * Local Rings, Semilocal Rings, and Idempotents, Perfect and Semiperfect Rings * Name Index * Subject Index