Lectures on Modules and Rings

Couverture
Springer Science & Business Media, 1999 - 557 pages
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).
 

Table des matières

Exercises for
17
Flat Modules and Homological Dimensions
121
Exercises for
122
Homological Dimensions
165
Injective Modules
207
Singular Submodules and Nonsingular Rings
246
Dense Submodules and Rational Hulls
272
Rings of Quotients
287
More Rings of Quotients
357
Martindale Rings of Quotients
383
Frobenius and QuasiFrobenius Rings
407
Frobenius Rings and Symmetric Algebras
422
60
443
Matrix Rings Categories of Modules and Morita Theory
459
Morita Theory of Category Equivalences
480
References
543

Classical Rings of Quotients
299
Right Goldie Rings and Goldies Theorems
320
Artinian Rings of Quotients
345

Autres éditions - Tout afficher

Expressions et termes fréquents

Fréquemment cités

Page 549 - On continuous rings and self-injective rings, Trans. Amer. Math. Soc. 118(1965), 158-173.

Informations bibliographiques