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交换代数·第1卷（英文版）

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交换代数·第1卷（英文版）

最 低 价：￥33.80

定 价：￥49.00

作 者：OscarZariski,PierreSamuel 著 著

出 版 社：世界图书出版公司

出版时间：2000-12-1

I S B N：9787506200585

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  • 交换代数·第1卷（英文版）
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  • 交换代数 第1卷（影印版）
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    内容简介
    This book is the child of an unborn parent. Some years ago the senior author began the preparation of a Colloquium volume on algebraic geometry, and he was then faced with the difficult task of incorporating in that volume the vast amount of purely algebraic material which is needed in abst algebraic geometry. The original .plan was to insert, from time to time, algebraic digressions in which concepts and results from commutative algebra were to be developed in full as and when they were needed. However, it soon became apparent that such a parenthetical treatment of the purely algebraic topics, covering a wide range of commutative algebra, would impose artificial bounds on the manner, depth, and degree of generality with which these topics could be treated. As is well known, abst algebraic geometry has been recently not only the main field of applications of commutative algebra but also the principal incentive of new research in commutative algebra. To approach the underlying algebra only in a strictly utilitarian, auxiliary, and parenthetical manner, to stop short of going further afield where the applications of algebra to algebraic geometry stop and the general algebraic theories inspired By geometry begin, impressed us increasingly as being a program scientifically too narrow and psychologically frustrating, not to mention the distracting effect that repeated algebraic digressions would inevitably have had on the reader, vis-h-vis the central algebro-geometrlc theme. Thus the idea of a separate book on commutative algebra was born, and the present book--of which this is the first of two volumes--is a realization of this idea, come to fruition at a time when its parent--a treatise on abst algebraic geometry-has still to see the light of the day.

    作者简介

    目录
    CHAPTER Ⅰ.INTRODUCTORY CONCEPTS
    1.Binary operations
    2.Groups
    3.Subgroups
    4.Abelian groups
    5.Rings
    6.Rings with identity
    7.Powers and multiples
    8.Fields
    9.Subrings and subfields
    10.Transformations and mappings
    11.Group homomorphisms
    12.Ring homomorphisms
    13.Identification of rings
    14.Unique factorization domains
    15.Euclidean domains
    16.Polynomials in one indeterminate
    17.Polynomial rings
    18.Polynomials in several indeterminates
    19.Quotient fields and total quotient rings
    20.Quotient rings with respect to multiplicative systems
    21.Vector spaces
    Ⅱ.ELEMENTO OF FIELD THEORY
    1.Field extensions
    2.Algebraic quanities
    3.Algebraic extensions
    4.The characteristic of field
    5.Separable and inseparable algebraic extensions
    6.Splitting fields and normal extensions
    7.The fundamental theorem of Galois theory
    8.Galois fields
    9.The theorem of the primitive element
    ……
    Ⅲ.IDEALS AND MODULES
    Ⅳ.NOETHERIAN RINGS
    Ⅴ.DEDEKIND DOMAING.CLASSICAL IDEALS THEORY
    INDEXL OF NOTATIONS
    INDEX OF DEFINITIONS

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