代數(shù)

內容概要

本書是Springer《數(shù)學研究生教材》第73卷，初版于1974年，30年來一直是美國及世界各國人學數(shù)學系采用的研究生代數(shù)教本。此書Springer已重印12次，由此證明這是一部經(jīng)典的研究生教材。全書取材適中，論述清晰，自成體系。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(huán)的結構理論等。書中有大量的練習和精心挑選的例子。

書籍目錄

PrefaceAcknowledgmentsSuggestions on the Use of This BookIntroduction: 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 NumbersChapter 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 & RelationsChapter 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 SeriesChapter 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 RingsChapter 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 nChapter VI: The Structure of FieldsChapter VII: Linear AlgebraChapter VIII: Commutative Rings and ModulesChapter IX: The Structure of RingsChapter X: CategoriesList of SymbolsBibliographyIndex

圖書封面

圖書標簽Tags

無

評論、評分、閱讀與下載

---

    代數(shù) PDF格式下載

---