代數（影印版） - 城邦阅读花园


	本書是Springer《數學研究生教材》第73卷，初版於1974年，30年來一直是美國及世界各國大學數學系採用的研究生代數教本。此書Springer已重印12次，由此證明這是一部經典的研究生教材。全書取材適中，論述清晰，自成系統。本書在一些問題的處理上有其獨到之處，如Sylow定理的證明、伽羅瓦理論的處理、可分域的擴張、環的結構理論等。書中有大量的練習和精心挑選的例子。



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	目錄 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 Zorn's 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