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Exercises in Classical Ring Theory

  • Book
  • © 2003

Overview

Authors:
  1. T. Y. Lam

    1. Department of Mathematics, University of California, Berkeley, Berkeley, USA

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Part of the book series: Problem Books in Mathematics (PBM)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xix
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  2. Wedderburn-Artin Theory

    Pages 1-48

  3. Jacobson Radical Theory

    Pages 49-97

  4. Introduction to Representation Theory

    Pages 99-140

  5. Prime and Primitive Rings

    Pages 141-200

  6. Introduction to Division Rings

    Pages 201-245

  7. Ordered Structures in Rings

    Pages 247-265

  8. Local Rings, Semilocal Rings, and Idempotents

    Pages 267-323

  9. Perfect and Semiperfect Rings

    Pages 329-347

  10. Back Matter

    Pages 349-359
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Keywords

About this book

" 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)

Authors and Affiliations

  • Department of Mathematics, University of California, Berkeley, Berkeley, USA

    T. Y. Lam

Bibliographic Information

  • Book Title: Exercises in Classical Ring Theory

  • Authors: T. Y. Lam

  • Series Title: Problem Books in Mathematics

  • DOI: https://doi.org/10.1007/b97448

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2003

  • Hardcover ISBN: 978-0-387-00500-3Published: 12 September 2003

  • Softcover ISBN: 978-1-4419-1829-1Published: 29 November 2010

  • eBook ISBN: 978-0-387-21771-0Published: 09 May 2006

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 2

  • Number of Pages: XX, 364

  • Topics: Commutative Rings and Algebras, Associative Rings and Algebras

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