| 本书是以Schaum的题解精萃《Abstract Algebra》为蓝本的同名英文教材。内容包括了目前近世代数的主要概念和基本结论，在复习和归纳的基础上稍微作了拓展，比如Zorn引理、Sylow定理等。还介绍了模的基本理论及其应用，对主理想整环上有限生成模的分解理论。考虑到抽象代数解题的困难，本书在每章后面精选了部分阅读材料，有些是正文内容的扩充，以帮助学生巩固基本理论和提高解题能力。 |
| 前言 Special Notation Chapter 1 Rudiments 1.1 Sets 1.2 Mappings 1.3 Relations and Operations 1.4 Reading Materials 1.5 Exercises Chapter 2 Groups 2.1 Introduction to Groups 2.2 Working with Groups 2.3 More on Group Structure 2.4 Reading Materials 2.5 Exercises Chapter 3 Rings 3.1 Basic Ring Structure 3.2 Ring Substructures 3.3 Specialized Rings 3.4 Working with Rings 3.5 Reading Materials 3.6 Exercises Chapter 4 Modules 4.1 Ring of Endomorphisms of an Abelian Group 4.2 Modules over Rings 4.3 Fundamental Concepts and Results 4.4 Free Modules 4.5 Direct Sum of Modules 4.6 Finitely Generated Modules over Principal Ideal Domains 4.7 Rational Canonical Form and Jordan Canonical Form 4.8 Reading Materials 4.9 Exercises Bibliography |
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