UID:
almahu_9949698046902882
Format:
1 online resource (569 p.)
ISBN:
1-281-76892-8
,
9786611768928
,
0-08-087446-0
Series Statement:
Pure and applied mathematics ; v. 127
Content:
Ring theory V1
Note:
"This is volume 127 in Pure and applied mathematics ..."
,
Front Cover; Ring Theory; Copyright Page; Contents; Foreword; Introduction: An Overview of Ring Theory; Table of Principal Notation; Chapter 0. General Fundamentals; 0.0 Preliminary Foundations; 0.1 Categories of Rings and Modules; 0.2 Finitely Generated Modules, Simple Modules, and Noetherian and Artinian Modules; 0.3 Abstract Dependence; Exercises; Chapter 1. Construction of Rings; 1.1 Matrix Rings and Idempotents; 1.2 Polynomial Rings; 1.3 Free Modules and Rings; 1.4 Products and Sums; 1.5 Endomorphism Rings and the Regular Representation
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1.6 Automorphisms, Derivations, and Skew Polynomial Rings1.7 Tensor Products; 1.8 Direct Limits and Inverse Limits; 1.9 Graded Rings and Modules; 1.10 Central Localization (also, cf. 2.12.9ff.); Exercises; Chapter 2. Basic Structure Theory; 2.1 Primitive Rings; 2.2 The Chinese Remainder Theorem and Subdirect Products; 2.3 Modules with Composition Series and Artinian Rings; 2.4 Completely Reducible Modules and the Socle; 2.5 The Jacobson Radical; 2.6 Nilradicals; 2.7 Semiprimary Rings and Their Generalizations; 2.8 Projective Modules (An Introduction)
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2.9 Indecomposable Modules and LE-Modules2.10 Injective Modules; 2.11 Exact Functors; 2.12 The Prime Spectrum; 2.13 Rings with Involution; Exercises; Chapter 3. Rings of Fractions and Embedding Theorems; 3.1 Classical Rings of Fractions; 3.2 Goldie's Theorems and Orders in Artinian Quotient Rings; 3.3 Localization of Nonsingular Rings and Their Modules; 3.4 Noncommutative Localization; 3.5 Left Noetherian Rings; Exercises; Chapter 4. Categorical Aspects of Module Theory; 4.1 The Morita Theorems; 4.2 Adjoints; Exercises
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Appendix A. The Proof of Magnus' Theorem and the Magnus-Witt Theorem (Theorem 1.3.38)Exercise; Appendix B. Normed Algebras and Banach Algebras; Exercises; The Basic Ring-Theoretic Notions and Their Characterizations; Major Ring- and Module-Theoretic Results Proved in Volume I (Theorems and Counterexamples; also cf. "Characterizations"); References; Subject Index; Pure and Applied Mathematics
,
English
Additional Edition:
ISBN 0-12-599841-4
Language:
English
