交换代数:英文
9787506292450
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作者艾森巴德
出版社世界图书出版公司出版社
ISBN9787506292450
出版时间2021-06
装帧平装
开本16开
页数785页
货号753730329263
上书时间2024-04-03
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商品名称
交换代数(影印版)
作者
(美)埃森巴德
责编
高蓉//李黎
定价
189.00
ISBN号
9787506292450
出版社
世界图书出版公司
版印次
1版 2次
开本
16开
装帧
平装
页数
785
出版时间
2008-05
印刷时间
2021-06
本书是Springer《Graduate Texts in Mathematics》系列丛书第150卷。为了更好的理解交换代数，运用几何的观点去研究交换代数，也就是代数几何学观点，是本书的一大特色。作者从基本观点——局部化以及自分解理论出发，通过对维数理论、微分理论、同调方法、自由解理论和对偶性的研究，强调该理论的出发点以及它们与数学其他部分的联系，练习中大量的引用强化了对该理论的理解。本书的还专门运用了一章来讲述Grobner基本观点以及基于这个关点的对交换代数以及代数几何很有建设性的方法。
Introduction
Advice for the Beginner
Information for the Expert
Prerequisites
Sources
Courses
A First Courses
A Second Courses
Acknowledgements
0 Elementary Definitions
0.1 Rings and Ideals
0.2 Unique Factorization
0.3 Modules
Ⅰ Basic Constructions
1 Roots of Commutative Algebra
1.1 Number Theory
1.2 Algebraic Curves and Fhnction Theory
1.3 Invariant Theory
1.4 The Basis Theorem
1.4.1 Finite Generation of Invariants
1.5 Graded Rings
1.6 Algebra and Geometry： The Nullstellensatz
1.7 Geometric Invariant Theory
1.8 Projective Varieties
1.9 Hilbert Functions and Polynomials
1.10 Free Resolutions and the Syzygy Theorem
1.11 Exercises
Noetherian Rings and Modules
An Analysis of Hilbert's Finiteness Argument
Some Rings of Invariants
Algebra and Geometry
Graded Rings and Projective Geometry
Hilbert Functions
Free Resolutions
Spec， max-Spec， and the Zariski Topology
2 Localization
2.1 Fractions
2.2 Horn and Tensor
2.3 The Construction of Primes
2.4 Rings and Modules of Finite Length
2.5 Products of Domains
2.6 Exercises
Z-graded Rings and Their Localizations
Partitions of Unity
Gluing
Constructing Primes
Idempotents， Products， and Connected Components
3 Associated Primes and Primary Decomposition
3.1 Associated Primes
3.2 Prime Avoidance
3.3 Primary Decomposition
3.4 Primary Decomposition and Factoriality
3.5 Primary Decomposition in the Graded Case
3.6 Extracting Information from Primary Decomposition
3.7 Why Primary Decomposition Is Not Unique
3.8 Geometric Interpretation of Primary Decomposition
3.9 Symbolic Powers and Functions Vanishing to High Order
3.9.1 A Determinantal Example
3.10 Exercises
General Graded Primary Decomposition
Primary Decomposition of Monomial Ideals
The Question of Uniqueness
Determinantal Ideals
……
Ⅱ Dimension Theory
Ⅲ Homological Methods
Appendix 1 Field Theory
Appendix 2 Multilinear Algebra
Appendix 3 Homological Algebra
Appendix 4 A Sketch of Local Cohomology
Appendix 5 Category Theory
Appendix 6 Limits and Colimits
Appendix 7 Where Next
Hints and Solutions for Selected Exercises
References
Index of Notation
Index
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