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.
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"As in the previous book, the presentation is extremely clear and incisive and the exercises are both interesting and challenging. Without a doubt, the book could indeed serve as a textbook for a very good---though definitely formidable---graduate course in ring theory. The author is the first to admit, in his introduction, that he is far from having covered all of the interesting topics in noncommutative ring theory. Therefore, given the high level of presentation of the two books he has already published, one can only hope that a third volume will be in the offing, despite his "solemn pledge" to the contrary."--MATHEMATICAL REVIEWS
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