抽象代数讲义-第1卷
温馨提示:5折以下图书主要为出版社尾货,大部分为全新(有塑封/无塑封),个别图书品相8-9成新、切口有划线标记、光盘等附件不全详细品相说明>>
- ISBN:9787510061516
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:24开
- 页数:217
- 出版时间:2013-10-01
- 条形码:9787510061516 ; 978-7-5100-6151-6
本书特色
《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(第1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。
内容简介
The present volume is the first of three that will be published under the general title Lectures in Abstract Algebra. These vol- umes are based on lectures which the author has gi,ren 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 sys- tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under- standing of a few topics is to be preferred to a superficial under- standing of many.
目录
SECTION
1. Operationsonsets
2. Product sets, mappings
3. Equivalencerelations
4. Thenaturalnumbers
5. Thesystemofintegers
6. The division process in I
CHAPTER I: SEMI-GROUPS AND GROUPS
1. Definition and examples ofsemi-groups
2. Non-associative binary compositions
3. Generalized associativelaw. Powers
4. Commutativity
5. Identities andinverses INTRODUCTION: CONCEPTS FROM SET THEORY THE SYSTEM OF NATURAL NUMBERS
SECTION
1. Operationsonsets
2. Product sets, mappings
3. Equivalencerelations
4. Thenaturalnumbers
5. Thesystemofintegers
6. The division process in I
CHAPTER I: SEMI-GROUPS AND GROUPS
1. Definition and examples ofsemi-groups
2. Non-associative binary compositions
3. Generalized associativelaw. Powers
4. Commutativity
5. Identities andinverses
6. Definition and examples of groups
7. Subgroups
8. Isomorphism
9. Transformation groups
10. Realization of a group as a transformation group
II. Cyclic groups. Order of an element
12. Elementary properties ofpermutations
13. Coset decompositions ofa group
14. Invariant subgroups and factor groups
15. Homomorphismofgroups
16. The fundamental theorem of homomorphism for groups
17. Endomorphisms, automorphisms, center of a group
18. Conjugatc classes
CHAPTER II: RINGS, INTEGRAL DOMAINS AND FIELDS
SECTION
1. Definition andexamples
2. Typesofrings
3. Quasi-regularity. The circle composition
4. Matrixrings
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 ofrings
10. Anti-isomorphism
11. Structure of the additive group of a ring. The charateristic ofaring
12. Algebra of subgroups of the additive group of a ring. Onr sidedideals
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. Polynomialrings
5. Structure of polynomial rings
6. Properties of the ring 2l[x]
7. Simple extensions ofa field
8. Structureofany field
9. The number of roots of a'polynomial in a field
10. Polynomials in several elements
11. Symmetric polynomials
12. Ringsoffunctions
CHAPTER IV: ELEMENTARY FACTORIZATlON THEORY
1. Factors, associates, irreducible elements
2. Gaussian semi-groups
3. Greatest common divisors
4. Principalidealdomains
……
CHAPTER V: GROUPS WITH OPERATORS
CHAPTER VI: MODULES AND IDEALS
CHAPTER VII: LATTICES
Index
节选
《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(第1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。
-
勒维特之星-大发现系列丛书
¥4.0¥16.0 -
喜马拉雅山珍稀鸟类图鉴
¥23.8¥68.0 -
昆虫的生存之道
¥19.1¥38.0 -
古文诗词中的地球与环境事件
¥8.4¥28.0 -
昆虫采集制作及主要目科简易识别手册
¥20.5¥50.0 -
声音简史
¥18.7¥52.0 -
物理学之美-插图珍藏版
¥30.4¥69.0 -
不匹配的一对:动物王国的性别文化
¥13.7¥42.8 -
现代物理学的概念和理论
¥23.1¥68.0 -
数学的魅力;初等数学概念演绎
¥13.0¥22.0 -
技术史入门
¥20.6¥48.0 -
改变世界的发现
¥15.4¥48.0 -
为了人人晓得相对论
¥4.6¥13.5 -
图说相对论(32开平装)
¥19.8¥46.0 -
舟山群岛植物图志
¥20.1¥59.0 -
宇宙与人
¥10.5¥35.0 -
数学专题讲座
¥11.0¥29.0 -
布尔巴基-数学家的秘密社团
¥11.4¥38.0 -
一代神话:哥本哈根学派
¥6.7¥15.5 -
考研数学高频考点精选题
¥1.2¥3.2