代数
目 录内容简介
Preface
Acknowledgments
Suggestions on the Use of This Book
Introduction： Prerequisites and Preliminaries
1. Logic
2. Sets and Classes
3. Functions
4. Relations and Partitions
5. Products
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Acknowledgments
Suggestions on the Use of This Book
Introduction： Prerequisites and Preliminaries
1. Logic
2. Sets and Classes
3. Functions
4. Relations and Partitions
5. Products
查看完整
目 录内容简介
《代数》是Springer《数学研究生教材》第73卷，初版于1974年，30年来一直是美国及世界各国人学数学系采用的研究生代数教本。此书Springer已重印12次，由此证明这是一部经典的研究生教材。全书取材适中，论述清晰，自成体系。《代数》在一些问题的处理上有其独到之处，如sylow定理的证明、伽罗瓦理论的处理、可分域的扩张，环的结构理论等。书中有大量的练习和精心挑选的例子。
目 录内容简介
Preface
Acknowledgments
Suggestions on the Use of This Book
Introduction： Prerequisites and Preliminaries
1. Logic
2. Sets and Classes
3. Functions
4. Relations and Partitions
5. Products
6. The Integers
7. The Axiom of Choice， Order and Zorns Lemma
8. Cardinal Numbers
Chapter I： Groups
1. Semigroups， Monoids and Groups
2. Homomorphisms and Subgroups
3. Cyclic.Groups
4. Cosets and Counting
5. Normality， Quotient Groups， and Homomorphisms
6. Symmetric， Alternating， and Dihedral Groups
7. Categories： Products， Coproducts， and Free Objects
8. Direct Products and Direct Sums
9， Free Groups， Free Products， Generators & Relations
Chapter II： The Structure of Groups
1. Free Abelian Groups
2. Finitely Generated Abelian Groups
3. The Krull-Schmidt Theorem
4. The Action of a Group on a Set
5. The Sylow Theorems
6. Classification of Finite Groups
7. Nilpotent and Solvable Groups
8. Normal and Subnormal Series
Chapter Ill： Rings
1. Rings and Homomorphisms
2. Ideals
3. Factorization in Commutative Rings
4. Rings of Quotients and Localization
5. Rings of Polynomials and Formal Power Series
6. Factorization in Polynomial Rings
Chapter IV： Modules
1. Modules， Homomorphisms and Exact Sequences
2. Free Modules and Vector Spaces
3. Projective and Injective Modules
4. Hom and Duality
5. Tensor Products
6. Modules over a Principal Ideal Domain
7. Algebras.
Chapter V： Fields and Galois Theory
1. Field Extensions
Appendix： Ruler and Compass Constructions
2. The Fundamental Theorem
Appendix： Symmetric Rational Functions
3. Splitting Fields， Algebraic Closure and Normality
Appendix： The Fundamental Theorem of Algebra..
4. The Galois Group of a Polynomial
5. Finite Fields
6. Separability：
7. Cyclic Extensions
8. Cyclotomic Extensions
9. Radical Extensions
Appendix： The General Equation of Degree n
Chapter VI： The Structure of Fields
Chapter VII： Linear Algebra
Chapter VIII： Commutative Rings and Modules
Chapter IX： The Structure of Rings
Chapter X： Categories
List of Symbols
Bibliography
Index
^ 收 起
Acknowledgments
Suggestions on the Use of This Book
Introduction： Prerequisites and Preliminaries
1. Logic
2. Sets and Classes
3. Functions
4. Relations and Partitions
5. Products
6. The Integers
7. The Axiom of Choice， Order and Zorns Lemma
8. Cardinal Numbers
Chapter I： Groups
1. Semigroups， Monoids and Groups
2. Homomorphisms and Subgroups
3. Cyclic.Groups
4. Cosets and Counting
5. Normality， Quotient Groups， and Homomorphisms
6. Symmetric， Alternating， and Dihedral Groups
7. Categories： Products， Coproducts， and Free Objects
8. Direct Products and Direct Sums
9， Free Groups， Free Products， Generators & Relations
Chapter II： The Structure of Groups
1. Free Abelian Groups
2. Finitely Generated Abelian Groups
3. The Krull-Schmidt Theorem
4. The Action of a Group on a Set
5. The Sylow Theorems
6. Classification of Finite Groups
7. Nilpotent and Solvable Groups
8. Normal and Subnormal Series
Chapter Ill： Rings
1. Rings and Homomorphisms
2. Ideals
3. Factorization in Commutative Rings
4. Rings of Quotients and Localization
5. Rings of Polynomials and Formal Power Series
6. Factorization in Polynomial Rings
Chapter IV： Modules
1. Modules， Homomorphisms and Exact Sequences
2. Free Modules and Vector Spaces
3. Projective and Injective Modules
4. Hom and Duality
5. Tensor Products
6. Modules over a Principal Ideal Domain
7. Algebras.
Chapter V： Fields and Galois Theory
1. Field Extensions
Appendix： Ruler and Compass Constructions
2. The Fundamental Theorem
Appendix： Symmetric Rational Functions
3. Splitting Fields， Algebraic Closure and Normality
Appendix： The Fundamental Theorem of Algebra..
4. The Galois Group of a Polynomial
5. Finite Fields
6. Separability：
7. Cyclic Extensions
8. Cyclotomic Extensions
9. Radical Extensions
Appendix： The General Equation of Degree n
Chapter VI： The Structure of Fields
Chapter VII： Linear Algebra
Chapter VIII： Commutative Rings and Modules
Chapter IX： The Structure of Rings
Chapter X： Categories
List of Symbols
Bibliography
Index
^ 收 起
目 录内容简介
《代数》是Springer《数学研究生教材》第73卷，初版于1974年，30年来一直是美国及世界各国人学数学系采用的研究生代数教本。此书Springer已重印12次，由此证明这是一部经典的研究生教材。全书取材适中，论述清晰，自成体系。《代数》在一些问题的处理上有其独到之处，如sylow定理的证明、伽罗瓦理论的处理、可分域的扩张，环的结构理论等。书中有大量的练习和精心挑选的例子。
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