代数(影印版)
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作者(美)Thomas W. Hungerford[著]
出版社世界图书出版有限公司北京分公司
ISBN9787519255695
出版时间2019-03
装帧平装
开本16开
定价149元
货号9528424
上书时间2024-11-20
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作者简介
本书作者（Thomas W. Hungerford）美国克利夫兰州立大学（Cleveland State University）数学系教授，著有《代数》等几十部教材或专著。
目录
Preface
Ackno w/edgmen ts
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 I1: The Structure of Groups
l. Free Abelian Groups
2. Finitely Generated Abelian Groups
3. The KruU-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 Ⅲ: 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 lnjective Modules
4. Horn and Duality
5. Tensor Products
6. Modules over a Principal Ideal Domain
7. Algebras
Chapter V: Fields and Galois Theory
I. 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
1. Transcendence Bases
2. Linear Disjointness and Separability
Chapter Ⅶ: Linear Algebra
1.Matrices and Maps
2. Rank and Equivalence Appendix: Abelian Groups Defined by Generators and Relations
3. Determinants
4. Decomposition of a Single Linear Transformation and Similarity.
5. The Characteristic Polynomial, Eigenvectors and "Eigenvalues
Chapter Ⅷ: Commutative Rings and Modules
1. Chain Conditions
2. Prime and Primary Ideals
3. Primary Decomposition
4. Noetherian Rings and Modules
5. Ring Extensions
6. Dedekind Domains
7. The Hilbert NullsteUensatz
Chapter IX: The Structure of Rings
1. Simple and Primitive Rings
2. The Jacobson Radical
3. Semisimple Rings
4. The Prime Radical; Prime and Semiprime Rings
5. Algebras
6. Division Algebras
Chapter X: Categories
1. Functors and Natural Transformations
2. Adjoint Functors
3. Morphisms
List of Symbols
Bibliography
index
精彩内容
目次：群和群的结构；环；模；域和伽罗瓦理论；域的结构；线性代数；交换环和模；环的结构；范畴论。
读者对象：数学专业研究生和科研人员．
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