- 交换代数教程(英文版)
- - 作者：(德)G.肯珀
  - 出版社：世界图书出版公司
  - ISBN：9787519211608
  - 出版日期：2016/05/01
  - 页数：264
- 售价：18

内容大纲
G.肯珀著的《交换代数教程（英文版）》是一部交换代数的教程，讲述清晰透彻，方法新颖，比较侧重交换代数的几何意义，但是比Eisenbud的大字典要好读一些，同时也有相当的深度。可以作为一到两学期的教程或者自学的不错选择。本书以整个几何背景一脉相承，围绕着本领域优选了一些很重要的概念和结果。能够使读者更深入地学习书中的知识。尽管强调理论，但还是有三章集中讨论计算方面。图例和练习使得书中的知识更加丰富。
作者介绍
目录
Introduction
Part I  The Algebra-Geometry Lexicon
  1  Hilbert's Nullstellensatz
    1.1  Maximal Ideals
    1.2  Jacobson Rings
    1.3  Coordinate Rings
    Exercises
  2  Noetherian and Artinian Rings
    2.1  The Noether and Artin Properties for Rings and Modules
    2.2 Noetherian Rings and Modules
    Exercises
  3  The Zariski Topology
    3.1  Affine Varieties
    3.2  Spectra
    3.3  Noetherian and Irreducible Spaces
    Exercises
  4  A Summary of the Lexicon
    4.1  True Geometry: Affine Varieties
    4.2  Abstract Geometry: Spectra
    Exercises
Part II  Dimension
  5  Krull Dimension and Transcendence Degree
    Exercises
  6  Localization
    Exercises
  7  The Principal Ideal Theorem
    7.1  Nal~yama's Lemma and the Principal Ideal Theorem
    7.2  The Dimension of Fibers
    Exercises
  8  Integral Extensions
    8.1  Integral Closure
    8.2  Lying Over, Going Up, and Going Down
    8.3  Noether Normalization
    Exercises
Part III  Computational Methods
  9  Grobner Bases
    9.1  Buchberger's Algorithm
    9.2  First Application: Elimination Ideals
    Exercises
  10  Fibers and Images of Morphisms Revisited
    10.1  The Generic Freeness Lemma
    10.2  Fiber Dimension and Constructible Sets
    10.3  Application: Invariant Theory
    Exercises
  11  Hilbert Series and Dimension
    11.1  The Hilbert-Serre Theorem
    11.2  Hilbert Polynomials and Dimension
    Exercises
Part IV  Local Rings
  12  Dimension Theory

    12.1  The Length of a Module
    12.2  The Associated Graded Ring
    Exercises
  13  Regular Local Rings
    13.1  Basic Properties of Regular Local Rings
    13.2  The Jacobian Criterion
    Exercises
  14  Rings of Dimension One
    14.1  Regular Rings and Normal Rings
    14.2  Multiplicative Ideal Theory
    14.3  Dedekind Domains
    Exercises
Solutions of Some Exercises
References
Notation
Index

内容大纲

作者介绍

目录

同类热销排行榜

推荐书目