An edition of A first course in noncommutative rings
(1991)
A first course in noncommutative rings
2nd ed.
by T. Y. Lam
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Book Details
Table of Contents
Machine generated contents note: CHAPTER 1
Wedderburn-Artin Theory
1. Basic Terminology and Examples
Exercises for 1
2. Semisimplicity
Exercises for 2
3. Structure of Semisimple Rings
Exercises for 3
CHAPTER 2
Jacobson Radical Theory
4. The Jacobson Radical
Exercises for 4
5. Jacobson Radical Under Change of Rings
Exercises for 5
6. Group Rings and the J-Semisimplicity Problem
Exercises for 6
CHAPTER 3
Introduction to Representation Theory
7. Modules over Finite-Dimensional Algebras
Exercises for 7
8. Representations of Groups
Exercises for 8
9. Linear Groups
Exercises for 9 CHAPTER 4
Prime and Primitive Rings
10. The Prime Radical; Prime and Semiprime Rings
Exercises for 10
11. Structure of Primitive Rings; the Density Theorem
Exercises for 11
12. Subdirect Products and Commutativity Theorems
Exercises for 12 CHAPTER 5
Introduction to Division Rings
13. Division Rings
Exercises for 13
14. Some Classical Constructions
Exercises for 14
15. Tensor Products and Maximal Subfields
Exercises for 15
16. Polynomials over Division Rings
Exercises for 16 CHAPTER 6
Ordered Structures in Rings
17. Orderings and Preorderings in Rings
Exercises for 17
18. Ordered Division Rings
Exercises for 18 CHAPTER 7
Local Rings, Semilocal Rings, and Idempotents
19. Local Rings
Exercises for 19
20. Semilocal Rings
Appendix: Endomorphism Rings of Uniserial Modules
Exercises for 20
21. Th Theory of Idempotents
Exercises for 21
22. Central Idempotents and Block Decompositions
Exercises for 22
CHAPTER 8
Perfect and Semiperfect Rings
23. Perfect and Semiperfect Rings
Exercises for 23
24. Homological Characterizations of Perfect and Semiperfect Rings
Exercises for 24
25. Principal Indecomposables and Basic Rings
Exercises for 25.
Edition Notes
Includes bibliographical references (p. 370-371) and index.
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| September 28, 2024 | Edited by MARC Bot | import existing book |
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| September 2, 2014 | Edited by Ana Tarazona | Edited without comment. |
| December 9, 2009 | Created by WorkBot | add works page |