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    • 出版时间:2014-03-01 00:00:00
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         https://product.suning.com/0070067633/11555288247.html

     

    商品参数
    • 作者: 无著
    • 出版社:其他
    • 出版时间:2014-03-01 00:00:00
    • 版次:1
    • 印次:1
    • 印刷时间:2014-03-01
    • 页数:653
    • 开本:24开
    • 装帧:平装
    • ISBN:9787510070228
    • 国别/地区:中国
    • 版权提供:其他

    李代数和代数群

    作  者:无 著
    定  价:99
    出 版 社:世界图书出版公司
    出版日期:2014年03月01日
    页  数:653
    装  帧:平装
    ISBN:9787510070228
    主编推荐

    内容简介

    The theory of groups and Lie algebras is interesting for many reasons. In the mathematical viewpoint, it employs at the same time algebra, analysis and geometry. On the other hand, it intervenes in other areas of science, in particular in different branches of physic8 and chemistry. It is an active domain of current research.
    The general theory of algebraic groupsnull

    作者简介

    精彩内容

    目录
      1 Results on topological spaces
    1.1 Irreducible sets and spaces
    1.2 Dimension
    1.3 Noetherian spaces
    1.4 Constructible sets
    1.5 Gluing topological spaces
    2 Rings and modules
    2.1 Ideals
    2.2 Prime and maximal ideals
    2.3 Rings of fractions and localization
    2.4 Localizations of modules
    2.5 Radical of an ideal
    2.6 Local rings
    2.7 Noetherian rings and modules
    2.8 Derivations
    2.9 Module of differentials
    3 Integral extensions
    3.1 Integral dependence
    3.2 Integrally closed domains
    3.3 Extensions of prime ideals
    4 Factorial rings
    4.1 Generalities
    4.2 Unique factorization
    4.3 Principal ideal domains and Euclidean domains
    4.4 Polynomials and factorial rings
    4.5 Symmetric polynomials
    4.6 Resultant and discriminant
    5 Field extensions
    5.1 Extensions
    5.2 Algebraic and transcendental elements
    5.3 Algebraic extensions
    5.4 Transcendence basis
    5.5 Norm and trace
    5.6 Theorem of the primitive element
    5.7 Going Down Theorem
    5.8 Fields and derivations
    5.9 Conductor
    6 Finitely generated algebras
    6.1 Dimension
    6.2 Noether's Normalization Theorem
    6.3 Krull's Principal Ideal Theorem*
    6.4 Maximal ideals
    6.5 Zariski topology
    7 Gradings and filtrations
    7.1 Graded rings and graded modules
    7.2 Graded submodules
    7.3 Applications
    7.4 Filtrations
    7.5 Grading associated to a filtration
     Inductive limits
    .1 Generalities
    .2 Inductive systems of maps
    .3 Inductive systems of magmas, groups and rings
    .4 An example
    .5 Inductive systems of algebras
    9 Sheaves of functions
    9.1 Sheaves
    9.2 Morphisms
    9.3 Sheaf associated to a presheaf
    9.4 Gluing
    9.5 Ringed space
    10 Jordan decomposition and some basic results on groups
    10.1 Jordan decomposition
    10.2 Generalities on groups
    10.3 Commutators
    10.4 Solvable groups
    10.5 Nilpotent groups
    ……
    11 Algebraic sets
    12 Prevarieties and varieties
    13 Projective varieties
    14 Dimension
    15 Morphisms and dimension
    16 Tangent paces
    17 Normal varieties
    18 Root systems
    19 Lie algebras
    20 Semisimple and reductive Lie algebras
    21 Algebraic groups
    22 Affine algebraic groups
    23 Lie algebra of an algebraic group
    24 Correspondence between groups and Lie algebras
    25 Homogeneous space and quotients
    38 Semisimple symmetric Lie algebras
    39 Sheets of Lie algebras,
    40 Index and linear forms
    References
    List of notations
    Index

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