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Exercises in Classical Ring Theory

 Buch
Besorgungstitel | Lieferzeit:3-5 Tage I
ISBN-13:
9780387005003
Einband:
Buch
Seiten:
364
Autor:
Tsit Yuen Lam
Gewicht:
680 g
Format:
242x163x26 mm
Serie:
Problem Books in Mathematics
Sprache:
Englisch
Beschreibung:

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.
This 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.

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.
This 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.
Autor: Tsit Yuen Lam
ISBN-13:: 9780387005003
ISBN: 0387005005
Verlag: Springer, Berlin
Gewicht: 680g
Seiten: 364
Sprache: Englisch
Auflage 2nd ed.
Sonstiges: Buch, 242x163x26 mm, XIX, 361 p.