基本信息 书名:抽象代数讲义 定价：49元 作者:雅格布斯 (Jacobson N.) 出版社：世界图书出版公司北京公司 出版日期：2013-10-01 ISBN：9787510061516 字数： 页码：217 版次：1 装帧：平装 开本：24开 商品重量： 编辑推荐 《抽象代数讲义》是一套久负盛名的三卷集教材，是作者雅格布斯根据他在霍普金斯大学和耶鲁大学讲课时的讲义编写而成的，后又成为作者《基本代数学》一书的蓝本。《抽象代数讲义（卷）》介绍了群、环、域、同构等抽象代数的重要的基本概念和抽象代数的基本性质。 内容提要 《抽象代数讲义(卷)(英文)》是一套久负盛名的三卷集教材，是作者根据他在霍普金斯大学和耶鲁大学讲课时的讲义编写而成的，后又成为作者的这一书的蓝本。卷介绍了群、环、域、同构等抽象代数的重要的基本概念和抽象代数的基本性质。第2卷主要涉及线性代数理论，着重论述了向量空间理论。第3卷介绍域理论和伽罗瓦理论，讨论了域的代数结构和域的赋值理论。 目录 INTRODUCTION： CONCEPTS FROM SET THEORY THE SYSTEM OF NATURAL NUMBERS 1. Operations on sets 2， Product sets， mappings 3. Equivalence relations 4. The natural numbers 5. The system of integers 6. The division process in I CHAPTER I： SEMI—CROUPS AND GROUPS 1. Definition and examples of semi—groups 2. Non—associative binary compositions 3. Generalized associative law. Powers 4. Commutativity 5. Identities and inverses 6. Definition and examples of groups 7. Subgroups " 8. Isomorphism 9. Transformation groups 10. Realization of a group as a transformation group 11. Cyclic groups. Order of an element 12. Elementary properties of permutations 13. Coset decompositions of a group 14. Invariant subgroups and factor groups 15. Homomorphism of groups 16. The fundamental theorem of homomorphism for groups 17. Endomorphisms， automorphisms， center of a group 18. Conjugate classes CHAPTER II： RINGS， INTEGRAL DOMAINS AND FIELDS SECTION 1. Definition and examples 2. Types of rings 3. Quasi—regularity. The circle composition 4. Matrix rings 5. Quaternions 6. Subrings generated by a set of elements. Center 7. Ideals， difference rings 8. Ideals and difference rings for the ring of integers 9. Homomorphism of rings 10. Anti—isomorphism 11. Structure of the additive group of a ring. The charateristic of a ring 12. Algebra of subgroups of the additive group of a ring. Onesided ideals 13. The ring of endomorphisms of a commutative group 14. The multiplications of a ring CHAPTER III： EXTENSIONS OF RINGS AND FIELDS 1. Imbedding of a ring in a ring with an identity 2. Field of fractions of a commutative integral domain 3. Uniqueness of the field of fractions 4. Polynomial rings 5. Structure of polynomial rings 6. Properties of the ring 7. Simple extensions of a field 8. Structure of any field 9. The number of roots of a polynomial in a field 10. Polynomials in several elements 11. Symmetric polynomials 12. Rings of functions CHAPTER IV： ELEMENTARY FACTORIZATION THEORY 1. Factors， associates， irreducible elements 2. Gaussian semi—groups 3. Greatest common divisors 4. Principal ideal domains SECTION 5. Euclidean domains 6. Polynomial extensions of Gaussian domains CHAPTER V： GROUPS WITH OPERATORS 1. Definition and examples of gr.oups with operators 2. M—subgroups， M—factor groups and M—homomorphisms 3. The fundamental theorem of homomorphism for M—groups 4. The correspondence between M—subgroups determined by a homomorphism 5. The isomorphism theorems for M—groups 6. Schreier's theorem 7. Simple groups and the Jordan—H61der theorem 8. The chain conditions 9. Direct products 10. Direct products of subgroups 11. Projections 12. Decomposition into indecomposable groups 13. The Krull—Schmidt theorem 14. Infinite direct products CHAPTER VI： MODULES AND IDEALS 1. Definitions 2. Fundamental concepts 3. Generators. Unitary modules 4. The chain conditions 5. The Hilbert basis theorem 6. Noetherian rings. Prime and primary ideals 7. Representation of an ideal as intersection of primary ideals 8. Uniqueness theorems 9. Integral dependence 10. Integers of quadratic fields CHAPTER VII： LATTICES 1. Partially ordered sets 2. Lattices 3. Modular lattices 4. Schreier's theorem. The chain conditions 5. Decomposition theory for latticeswith ascending chain condition 6. Independence 7. Complemented modular lattices 8. Boolean algebras Index 作者介绍
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