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Field name	Details
Dewey Class	512.4
Title	Lectures on Modules and Rings ([EBook]) / by T. Y. Lam.
Author	Lam, T. Y. (Tsit-Yuen)
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 1999.
Physical Details	XXIII, 557 pages : online resource.
Series	Graduate texts in mathematics 0072-5285 ; ; 189
ISBN	9781461205258
Summary Note	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 too late! My writing project in ring theory started in 1983 after I taught a year-long course in the subject at Berkeley. My original plan was to write up my lectures and publish them as a graduate text in a couple of years. My hopes of carrying out this plan on schedule were, however, quickly dashed as I began to realize how much material was at hand and how little time I had at my disposal. As the years went by, I added further material to my notes, and used them to teach different versions of the course. Eventually, I came to the realization that writing a single volume would not fully accomplish my original goal of giving a comprehensive treatment of basic ring theory. At the suggestion of Ulrike Schmickler-Hirzebruch, then Mathematics Editor of Springer-Verlag, I completed the first part of my project and published the write up in 1991 as A First Course in Noncommutative Rings, GTM 131, hereafter referred to as First Course (or simply FC).:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-0525-8
Links to Related Works	Subject References: Algebra . Modules (Algebra) . Rings (Algebra) . Authors: Lam, T. Y. (Tsit-Yuen) . Lam, T. Y. (Tsit-Yuen) . Corporate Authors: SpringerLink (Online service) . Series: Graduate texts in mathematics . GTM . Classification: 512.4 .

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Lectures on Modules and Rings

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