Lectures on Modules and Rings
Textbook writing must be one of the cruelest of self-inflicted tortures. - Carl Faith Math Reviews 54: 5281 So why didn't I heed the warning of a wise colleague, especially one who is a great expert in the subject of modules and rings? The answer is simple: I did not learn about it until it was...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1999, 1999
|
| Edition: | 1st ed. 1999 |
| Series: | Graduate Texts in Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Free Modules, Projective, and Injective Modules
- 1. Free Modules
- 2. Projective Modules
- 3. Injective Modules
- 31. Matlis’ Theory
- 2 Flat Modules and Homological Dimensions
- 4. Flat and Faithfully Flat Modules
- 41. Faithfully Flat Modules
- 5. Homological Dimensions
- 3 More Theory of Modules
- 6. Uniform Dimensions, Complements, and CS Modules
- 7. Singular Submodules and Nonsingular Rings
- 8. Dense Submodules and Rational Hulls
- 4 Rings of Quotients
- 9. Noncommutative Localization
- 10. Classical Rings of Quotients
- 11. Right Goldie Rings and Goldie’s Theorems
- 12. Artinian Rings of Quotients
- 5 More Rings of Quotients
- 13. Maximal Rings of Quotients
- 14. Martindale Rings of Quotients
- 6 Frobenius and Quasi-Frobenius Rings
- 15. Quasi-Frobenius Rings
- 16. Frobenius Rings and Symmetric Algebras
- 7 Matrix Rings, Categories of Modules, and Morita Theory
- 17. Matrix Rings
- 18. Morita Theory of Category Equivalences
- 19. Morita Duality Theory
- References
- Name Index