华罗庚文集 代数卷 II

出版时间：2011-2  出版社：科学出版社  作者：华罗庚  页数：376  译者：李福安 注解  
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内容概要

　　本书汇集了华罗庚先生1930—1952年关于代数和矩阵几何的代表性论文22篇，以及万哲先关于华罗庚在代数和几何领域成就的一篇介绍文章。
　　华罗庚的论文内容深刻，技巧性很强，要求的预备知识并不多．本书适合数学专业的研究生和研究人员阅读，大学数学系的高年级学生也能读懂其中大部分内容。

书籍目录

《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. II. 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 any field
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 Dieudonn 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

章节摘录

版权页：插图：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.

编辑推荐

《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。

用户评论 (总计6条)

•   华罗庚是国际数学大师，是中国解析数论、矩阵几何学、典型群、自守函数论等多方面研究的创始人和开拓者。他在多复变函数论、矩阵几何学方面的卓越贡献，更是影响到了世界数学的发展。也有国际上有名的“典型群中国学派”，华罗庚先生在多复变函数论，典型群方面的研究领先西方数学界10多年，这些研究成果被著名的华裔数学家丘成桐高度称赞。华罗庚先生是难以比拟的天才。 由中国科学院华罗庚数学重点实验室、中国科学院研究生院华罗庚数学研究中心编纂、由科学出版社出版的《华罗庚文集 代数卷 II》适合数学及相关专业大学生、研究生、教师及科研人员阅读参考，数学后辈珍藏。
•   当然是非常好！
•   华老代数方面的一些文章， 很棒的！
•   推荐这本书 大师之作 写的很经典 把代数的东西写的很具体
•   还没有仔细看啊!不错。
•   其中不少是对卷1典型群的补充，一直想看的文章.