《基礎代數》是2015年5月世界圖書出版公司出版的圖書，作者是卡恩（Cohn，P.M.）。本書主要是涵蓋了代數的所有重要結果。
基本介紹
- 書名：基礎代數
- 作者：卡恩（Cohn，P.M.）
- 出版社：世界圖書出版公司
- ISBN：9787510094644
內容簡介,圖書目錄,作者簡介,
內容簡介
本書是P.M.Cohn的經典的三卷集代數教材的修訂恥寒龍版卷，被廣大讀者所追捧，公認為學習代數入門教材的傑出代表。本書中涵蓋了代數的所有重要結果。讀者具備一定的線性代數、群和域知識，對理解本書將更有益。本卷次的目次：集合；群；格點全催和範疇；環和模；凶樂微臭代數；多線性代數；域論；二次型和有序域；賦值論；交換環；無限域擴展。
棗旋狼讀者對象辯簽兆：數學專業的廣戒判籃大師生。
圖書目錄
Preface
Conventions on Terminology
1.Sets
1.1 Finite， Countable and Uncountable Sets
1，再檔榜白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
作者簡介
P.M.Cohn(P.M.卡恩,英國)是國際知名學者，在數學和物理學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用於科研工作者、高校教師和研究生。
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
作者簡介
P.M.Cohn(P.M.卡恩,英國)是國際知名學者，在數學和物理學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用於科研工作者、高校教師和研究生。
