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Lectures on modules and rings
1st ed. 1999, [1999]

Details

Autor(en) / Beteiligte
Titel
Lectures on modules and rings
Auflage
1st ed. 1999
Ort / Verlag
Berlin ; : Springer-Verlag,
Erscheinungsjahr
[1999]
Link zum Volltext
Beschreibungen/Notizen
  • Bibliographic Level Mode of Issuance: Monograph
  • Includes bibliographical references at the end of each chapters and indexes.
  • 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.
  • 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 writeup in 1991 as A First Course in Noncommutative Rings, GTM 131, hereafter referred to as First Course (or simply FC).
  • English
  • Description based on print version record.
Sprache
Englisch
Identifikatoren
ISBN: 1-4612-0525-5
DOI: 10.1007/978-1-4612-0525-8
Titel-ID: 9925031349006463
Format
1 online resource (XXIII, 557 p.)
Schlagworte
Modules (Algebra)