A first course in noncommutative rings
By: T.Y. Lam.
Edition: 2nd ed.
Series: Graduate texts in mathematics ;; 131
Publisher: Springer
Published: 2001
Place of publication: New York
Language: eng
Number of pages: 385
Subjects: Noncommutative rings
Notes: Includes bibliographical references (p. 370-371) and index.
Table of contents: title: Machine generated contents note: CHAPTER 1; title: Wedderburn-Artin Theory; title: 1. Basic Terminology and Examples; title: Exercises for 1; title: 2. Semisimplicity; title: Exercises for 2; title: 3. Structure of Semisimple Rings; title: Exercises for 3; title: CHAPTER 2; title: Jacobson Radical Theory; title: 4. The Jacobson Radical; title: Exercises for 4; title: 5. Jacobson Radical Under Change of Rings; title: Exercises for 5; title: 6. Group Rings and the J-Semisimplicity Problem; title: Exercises for 6; title: CHAPTER 3; title: Introduction to Representation Theory; title: 7. Modules over Finite-Dimensional Algebras; title: Exercises for 7; title: 8. Representations of Groups; title: Exercises for 8; title: 9. Linear Groups; title: Exercises for 9 CHAPTER 4; title: Prime and Primitive Rings; title: 10. The Prime Radical; Prime and Semiprime Rings; title: Exercises for 10; title: 11. Structure of Primitive Rings; the Density Theorem; title: Exercises for 11; title: 12. Subdirect Products and Commutativity Theorems; title: Exercises for 12 CHAPTER 5; title: Introduction to Division Rings; title: 13. Division Rings; title: Exercises for 13; title: 14. Some Classical Constructions; title: Exercises for 14; title: 15. Tensor Products and Maximal Subfields; title: Exercises for 15; title: 16. Polynomials over Division Rings; title: Exercises for 16 CHAPTER 6; title: Ordered Structures in Rings; title: 17. Orderings and Preorderings in Rings; title: Exercises for 17; title: 18. Ordered Division Rings; title: Exercises for 18 CHAPTER 7; title: Local Rings, Semilocal Rings, and Idempotents; title: 19. Local Rings; title: Exercises for 19; title: 20. Semilocal Rings; title: Appendix: Endomorphism Rings of Uniserial Modules; title: Exercises for 20; title: 21. Th Theory of Idempotents; title: Exercises for 21; title: 22. Central Idempotents and Block Decompositions; title: Exercises for 22; title: CHAPTER 8; title: Perfect and Semiperfect Rings; title: 23. Perfect and Semiperfect Rings; title: Exercises for 23; title: 24. Homological Characterizations of Perfect and Semiperfect Rings; title: Exercises for 24; title: 25. Principal Indecomposables and Basic Rings; title: Exercises for 25.