本书系统地介绍抽象代数的基础内容，包括群、环、域、模等，每一部分独立成章，本科生、研究生等不同层次的读者可以挑选阅读。书中范例丰富，风趣易懂；另外，每一小节后都配有一定数量、难易不等的习题，书后还附有解答与提示，便于教学和自学。

与第2版相比，第3版的更新如下：阐述更清晰，表达更顺畅。在前五章中，最重要的节、小节、定义、定理、例子旁边加有箭头指示。包含了任意域上的线性代数的更多知识。增加了一节介绍分类平面上的楣(frieze)群。增加了100多道习题。本书可供高等院校数学系师生及相关工程技术人员使用。

  本书系统地介绍了抽象代数的基础内容，包括群、环、域、模等，每一部分独立成章，本科生、研究生等不同层次的读者可以挑选阅读。书中范例丰富，风趣易懂；另外，每一小节后都配有一定数量、难易不等的习题，书后还附有解答与提示，便于教学和自学。

本书可供高等院校数学系师生及有关工程技术人员使用。

Preface to the Third Edition

Suggested Syllabi

To the Reader

Chapter I Number Theory

  Section 1.1 Induction

  Section 1.2 Binomial Theorem and Complex Numbers

  Section 1.3 Greatest Common Divisors

  Section 1.4 The Fundamental Theorem of Arithmetic

 Section 1.5 Congruences

 Section 1.6 Dates and Days

Chapter 2 Groups I

 Section 2.1 Some Set Theory

  Functions

  Equivalence Relations

 Section 2.2 Permutations 

 Section 2.3 Groups

  Symmetry

 Section 2.4 Subgroups and Lagrange's Theorem 

 Section 2.5 Homomorphisms

 Section 2.6 Quotient Groups

 Section 2.7 Group Actions

 Section 2.8 Counting with Groups

Chapter 3 Commutative Rings I

 Section 3.1 First Properties

 Section 3.2 Fields

 Section 3.3 Polynomials

 Section 3.4 Homomorphisms

 Section 3.5 From Numbers to Polynomials .

  Euclidean Rings

 Section 3.6 Unique Factorization

 Section 3.7 Irreducibility

 Section 3.8 Quotient Rings and Finite Fields

 Section 3.9 A Mathematical Odyssey

  Latin Squares

  Magic Squares

  Design of Experiments

  Projective Planes

Chapter 4 Linear Algebra

  Section 4.1 Vector Spaces

  Gaussian Elimination

 Section 4.2 Euclidean Constructions

 Section 4.3 Linear Transformations

 Section 4.4 Eigenvalues

 Section 4.5 Codes

  Block Codes

  Linear Codes

  Decoding

Chapter 5 Fields

 Section 5.1 Classical Formulas

  Viete's Cubic Formula

 Section 5.2 Insolvability of the General Quintic

  Formulas and Solvability by Radicals 

  Quadratics

  Cubics

  Quartics

  Translation into Group Theory

 Section 5,3 Epilog

Chapter 6 Groups H

 Section 6.1 Finite Abelian Groups

 Section 6.2 The Sylow Theorems

 Section 6.3 Ornamental Symmetry

Chapter 7 Commutative Rings II

 Section 7.1 Prime Ideals and Maximal Ideals

  Section 7.2 Unique Factorization

 Section 7.3 Noetherian Rings

 Section 7.4 Varieties

 Section 7.5 Generalized Divison Algorithm .

  Monomial Orders

  Division Algorithm

 Section 7.6 Grobner Bases

Appendix A Inequalities

Appendix B Pseudocodes

Hints for Selected Exercises

Bibliography

Index