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  • ISBN:9787506292450
  • 装帧:一般纯质纸
  • 册数:暂无
  • 重量:暂无
  • 开本:16开
  • 页数:785
  • 出版时间:2008-05-01
  • 条形码:9787506292450 ; 978-7-5062-9245-0

内容简介

本书是Springer“数学研究生教材”第150卷,为了更好的理解交换代数,运用几何的观点,即代数几何学观点去研究交换代数,是本书的一大特色。作者从基本概念——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,强调这些理论的出发点以及它们与数学其它分支的联系,书中的大量练习更强化了对读者对这些理论的理解。

目录

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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作者简介

D.Eisenbud,加利福尼亚大学(University of California)数学系教授。加州大学,位于美国加州的一个由数所公立大学组成的大学系统,也是世界上影响较大力的公立大学系统,被誉为"世界*好的公立大学"和"公立高等教育的典范"。

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