Lectures on modules and rings

Includes index

Includes bibliography (p. 543-552) and references

1. Free Modules, Projective, and Injective Modules. 1. Free Modules. 2. Projective Modules. 3. Injective Modules 2. Flat Modules and Homological Dimensions. 4. Flat and 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.

This book provides a new alternative introduction to the theory of modules and rings that is largely independent of the author's earlier graduate text, A First Course in Noncommutative Rings (GTM 131). Developed from the author's lectures given over the years at Berkeley, this text is ideally suited for use in graduate courses and seminars, as well as for self-study and general reference. Focusing on some of the most central topics in modules and rings, the author efficiently introduces the reader to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions.