Exercises in Classical Ring Theory

1. Front Matter

   Pages i-xix

   PDF

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

    PDF

" 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)

• algebra
• category theory
• field
• representation theory
• ring theory

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

  T. Y. Lam

Policies and ethics