Lectures on Modules and RingsSpringer 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
artinian ring assume automorphism Baer ring cogenerator commutative domain commutative noetherian commutative ring complement Corollary defined direct sum direct summand division ring embedded endomorphism example Exercise exists f.g. projective fact faithfully flat finite flat modules following are equivalent Frobenius algebras functor Goldie ring hence idempotent implies indecomposable injective hull injective modules isomorphism k-algebra left ideal left R-module Lemma M₁ matrix nilpotent noetherian ring nonsingular ring nonzero notation notion polynomial prime ideal Proof Proposition prove QF ring Qmax R-homomorphism r.gl.dim R)-bimodule regular elements resp result right annihilators right artinian ring right Goldie ring right ideal right noetherian ring right nonsingular right R-module right self-injective ring of quotients self-injective ring semihereditary semiprime ring semisimple ring short exact sequence soc(RR submodule subring subsection surjective Theorem theory u.dim uniform dimension X-Inn(R Z(RR
Fréquemment cités
Page 549 - On continuous rings and self-injective rings, Trans. Amer. Math. Soc. 118(1965), 158-173.
Références à ce livre
Frobenius and Separable Functors for Generalized Module ..., Numéro 1787 Stefaan Caenepeel,Gigel Militaru,Shenglin Zhu Aucun aperçu disponible - 2002 |
Self-Dual Codes and Invariant Theory Gabriele Nebe,Eric M. Rains,Neil J. A. Sloane Aperçu limité - 2006 |