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  • 华罗庚文集:代数卷2[精装]
  • 共2个商家     71.50元~80.40
  • 作者:华罗庚(作者),李福安(注释解说词)
  • 出版社:科学出版社;第1版(2011年2月1日)
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  • ISBN:9787030300140

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    《华罗庚文集:代数卷2》:中国科学院华罗庚数学重点实验室丛书。

    目录

    《华罗庚文集》序言
    algebra and geometry
    苏家驹之代数的五次方程式解法不能成立之理由
    geometries of matrices. i. generalizations of von staudt's theorem
    geometries of matrices. il. arithmetical construction
    orthogonal classification of hermitian matrices
    geometries of matrices. ii. study of involutions in the geometry of symmetric matrices
    geometries of matrices. iii. fundamental theorems in the geometries of symmetric matrices
    some “anzahl” theorems for groups of prime power orders
    on the automorphisms of the symplectic group over anyfield
    on the existence of solutions of certatin equations in a finite field
    characters over certain types of rings with applications to the theory of equations in a finite field
    on the automorphisms of a sfield
    on the number of solutions of some trinomial equations in a finite field
    on the nature of the solutions of certain equations in a finite field
    some properties of a sfield
    on the generators of the symplectic modular group
    geometry of symmetric matrices over any field with characteristic other than two
    on the multiplicative group of a field
    环之准同构及对射影几何的一应用
    a theorem on matrices over a sfield and its applications
    supplement to the paper of dieudonne on the automorphisms of classical groups
    automorphisms of the unimodular group
    automorphisms of the projective unimodular group
    《华罗庚文集》已出版书目

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    It was first shown in the author's recent investigations on the theory of auto-morphic functions of a matrix-variable that there are three types of geometry playingimportant roles. Besides their applications, the author obtained a great many resultswhich seem to be interesting in themselves.
    The main object of the paper is to generalize a theorem due to von Staudt, whichis known as the fundamental theorem of the geometry in the complex domain. Thestatement of the theorem is:
    Every topological transformation of the complex plane into itself, which leavesthe relation of harmonic separation invariant, is either a eollineation or an anti-collineation.
    Since the fields and groups may be varied, several generalizations of vonStaudt's theorem will be given. The proofs of the theorems have interestingcorollaries.
    The paper contains also some fundamental results which will be useful in suc-ceeding papers.