 | 书 名: 抽象代数讲义 第1卷(英文版)
作 者:
出 版 社: 世界图书出版公司北京公司
ISBN : 750620060
原 价: ￥36
 有一家网站低于85折正在热销 | 抽象代数讲义 第1卷(英文版)-图书目录:
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-GROUPS 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 III 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 charateristie
of a ring
12. Algebra of subgroups of the additive group of a ring. One-
sided 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 [x]
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
5. Euclidean domains
6. Polynomial extensions of Gaussian domains
CHAPTER V; GROUPS WITH OPERATORS
1. Definition and examples of groups 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
S, The isomorphism theorems for M-groups
6. Schreiers theorem
7. Simple groups and the Jordan-Holder 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. Schreiers theorem. The chain conditions
5. Decomposition theory for lattices with ascending chain conadition
6. Independence
7. Complemented modular lattices
8. Boolean algebras
Index
抽象代数讲义 第1卷(英文版)-图书简介:
The present volume is the first of three that will be published under the general title Lectures in .dbstract Algebra. These vol umes are based on lectures which the at, thor has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale University. The general plan of the work is as follows: The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraic concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond the foundations and elementary properties of the algebraic systems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper understanding of a few topics is to be preferred to a superficial understanding of many.
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