抽象代数基本教程-(第7版) 目录

Instructor's Preface
Student's Preface
Dependence Chart
Sets and Relations
Ⅰ GROUPS AND SUBGROUPS
Introduction and Examples
Binary Operations
Isomorphic Binary Structures
Groups
Subgroups
Cyclic Groups
Generating Sets and Cayley Digraphs
Ⅱ PERMUTATIONS, COSETS, AND DIRECT PRODUCTS
Groups of Permutations
Orbits, Cycles, and the Alternating Groups
Cosets and the Theorem of Lagrange
Direct Products and Finitely Generated Abelian Groups
Plane Isometries
Ⅲ HOMOMORPHISMS AND FACTOR GROUPS
Homomorphisms
Factor Groups
Factor-Group Computations and Simple Groups
Group Action on a Set
Applications of G-Sets to Counting
Ⅳ RINGS AND FIELDS
Rings and Fields
Integral Domains
Fermat's and Euler's Theorems
The Field of Quotients of an Integral Domain
Rings of Polynomials
Factorization of Polynomials over a Field
Noncommutative Examples
Ordered Rings and Fields
Ⅴ IDEALS AND FACTOR RINGS
Homomorphisms and Factor Rings
Prime and Maximal Ideals
Grobner Bases for Ideals
Ⅵ EXTENSION FIELDS
Introduction to Extension Fields
Vector Spaces
Algebraic Extensions
Geometric Constructions
Finite Fields
Ⅶ ADVANCED GROUP THEORY
Isomorphism Theorems
Series of Groups
Sylow Theorems
Applications of the Sylow Theory
Free Abelian Groups
Free Groups
Group Presentations
Ⅷ GROUPS IN TOPOLOGY
Simplicial Complexes and Homology Groups
Computations of Homology Groups
More Homology Computations and Applications
Homological Algebra
Ⅸ FACTORIZATION
Unique Factorization Domains
Euclidean Domains
Gaussian Integers and Multiplicative Norms
Ⅹ AUTOMORPHISMS AND GALOIS THEORY
Automorphisms of Fields
The Isomorphism Extension Theorem
Splitting Fields
Separable Extensions
Totally Inseparable Extensions
Galois Theory
Illustrations of Galois Theory
Cyclotomic Extensions
Insolvability of the Quintic
Appendix: Matrix Algebra
Bibliography
Notations
Answers to Odd-Numbered Exercises Not Asking for Definitions or Proofs
Index

抽象代数基本教程-(第7版) 内容简介

本书是一部介绍抽象代数的入门书籍。假定学生了解了微积分和线性代数,并且理论大都在书中以例子和练习的形式出现。该书旨在教给学生尽可能多的群，环，以及域理论，*大特点是包含了较多的扎实的基础部分，这些部分对于更进一步的学习代数是有很大的帮助的。为了满足更多读者的要求，本书包含了很多有关拓扑中的同调群，同调群的计算以加深对因子群的理解。书中内容浅显易懂，为了将同调群讲述的更加清楚，在第6版的基础上减少了自动机，二进制线性密码以及部分代数结构。书后面附有不少练习，这些加深学生对内容的理解。目次：群与子群；排列，陪集和直积；同态和因子群；环和域；理想和因子环；扩展域；高等群论；拓扑群；因子分解；自同态和伽罗瓦理论。

抽象代数基本教程-(第7版) 节选

《抽象代数基本教程》是一部介绍抽象代数的入门书籍。假定学生了解了微积分和线性代数，并且理论大都在书中以例子和练习的形式出现。该书旨在教给学生尽可能多的群，环，以及域理论，*大特点是包含了较多的扎实的基础部分，这些部分对于更进一步的学习代数是有很大的帮助的。为了满足更多读者的要求，《抽象代数基本教程》包含了很多有关拓扑中的同调群，同调群的计算以加深对因子群的理解。书中内容浅显易懂，为了将同调群讲述的更加清楚，在第6版的基础上减少了自动机，二进制线性密码以及部分代数结构。书后面附有不少练习，这些加深学生对内容的理解。