- 基础代数(英文版)
- - 作者：(英)卡恩
  - 出版社：世界图书出版公司
  - ISBN：9787510094644
  - 出版日期：2015/05/01
  - 页数：465
- 售价：31.2

内容大纲
《基础代数(英文版)》是P. M. Cohn(卡恩)的经典的三卷集代数教材的修订版第一卷，被广大读者所追捧，公认为学习代数入门教材的杰出代表。本书中涵盖了代数的所有重要结果。读者具备一定的线性代数、群和域知识，对理解本书将更有益。本卷次的目次：集合；群；格点和范畴；环和模；代数；多线性代数；域论；二次型和有序域；赋值论；交换环；无限域扩展。
读者对象：数学专业的广大师生。
作者介绍
目录
Preface
Conventions on Terminology
1.Sets
  1.1 Finite， Countable and Uncountable Sets
  1.2 Zom's Lemma and Well—ordered Sets
  1.3 Graphs
2.Groups
  2.1 Definition and Basic Properties
  2.2 Permutation Groups
  2.3 The Isomorphism Theorems
  2.4 Soluble and Nilpotent Groups
  2.5 Commutators
  2.6 The Frattini Subgroup and the Fitting Subgroup
3.Lattices and Categories
  3.1 Definitions； Modular and Distributive Lattices
  3.2 Chain Conditions
  3.3 Categories
  3.4 Boolean Algebras
4.Rings and Modules
  4.1 The Definitions Recalled
  4.2 The Category of Modules over a Ring
  4.3 Semisimple Modules
  4.4 Matrix Rings
  4.5 Direct Products of Rings
  4.6 Free Modules
  4.7 Projective and Injective Modules
  4.8 The Tensor Product of Modules
  4.9 Duality of Finite Abelian Groups
5.Algebras
  5.1 Algebras； Definition and Examples
  5.2 The Wedderbum Structure Theorems
  5.3 The Radical
  5.4 The Tensor Product of Algebras
  5.5 The Regular Representation； Norm and Trace
  5.6 M6bius Functions
6.Muhilinear Algebra
  6.1 Graded Algebras
  6.2 Free Algebras and Tensor Algebras
  6.3 The Hilbert Series of a Graded Ring or Module
  6.4 The Exterior Algebra on a Module
7.Field Theory
  7.1 Fields and their Extensions
  7.2 Splitting Fields
  7.3 The Algebraic Closure of a Field
  7.4 Separability
  7.5 Automorphisms of Field Extensions
  7.6 The Fundamental Theorem of Galois Theory
  7.7 Roots of Unity
  7.8 Finite Fields
  7.9 Primitive Elements； Norm and Trace

  7.10 Galois Theory of Equations
  7.11 The Solution of Equations by Radicals
8.Quadratic Forms and Ordered Fields
  8.1 Inner Product Spaces
  8.2 Orthogonal Sums and Diagonalization
  8.3 The Orthogonal Group of a Space
  8.4 The Clifford Algebra and the Spinor Norm
  8.5 Witt's Cancellation Theorem and the Witt Group of a Field
  8.6 Ordered Fields
  8.7 The Field of Real Numbers
  8.8 Formally Real Fields
  8.9 The Witt Ring of a Field
  8.10 The Symplectic Group
  8.11 Quadratic Forms in Characteristic Two
9.Valuation Theory
  9.1 Divisibility and Valuations
  9.2 Absolute Values
  9.3 The p—adic Numbers
  9.4 Integral Elements
  9.5 Extension of Valuations
10.Commutative Rings
  10.1 Operations on Ideals
  10.2 Prime Ideals and Factorization
  10.3 Localization
  10.4 Noetherian Rings
  10.5 Dedekind Domains
  10.6 Modules over Dedekind Domains
  10.7 Algebraic Equations
  10.8 The Primary Decomposition
  10.9 Dimension
  10.10 The Hilbert Nullstellensatz
11.Infinite Field Extensions
  11.1 Abstract Dependence Relations
  11.2 Algebraic Dependence
  11.3 Simple Transcendental Extensions
  11.4 Separable and p—radical Extensions
  11.5 Derivations
  11.6 Linearly Disjoint Extensions
  11.7 Composites of Fields
  11.8 Infinite Algebraic Extensions
  11.9 Galois Descent
  11.10 Kummer Extensions
Bibliography
List of Notations
Author Index
Subject Index

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