环上矩阵几何（英文版）

图书标准信息

• 作者 Huang Liping 著
• 出版社 科学出版社
• 出版时间 2006-08
• 版次 1
• ISBN 9787030169822
• 定价 60.00元
• 装帧 平装
• 开本 其他
• 纸张 其他
• 页数 340页

【内容简介】

　　环与模，环上矩阵论，非交换主理想整环上的仿射几何与射影几何，非交换主理想整环上的长方矩阵几何，交换主理想整环上的对称矩阵几何，除环上Hermitian矩阵几何，除环上分块三角矩阵几何，以及矩阵几何在代数学、几何学、图论等方面的应用。

【目录】

Preface
Notation
Chapter1RingsandModules
1.1Rings
1.2ModulesandK-algebras
1.3Principalidealdomains
1.4SemisimpleringsandJacobsonsemisimplerings
1.5Ringswithinvolution
Chapter2MatricesandModulesoverRing
2.1Matrixoverring
2.2Semifir，HermiteringsandBezoutdomains
2.3Therankofmatrices
2.4ElementaryoperationsandreductionofmatricesoverPID
2.5Hermitianandsymmetricmatrices
2.6Deternfinantsovercommutativering
Chapter3AftmeGeometryandProjectiveGeometryoverRing
3.1Subspacesoffreemodule
3.2SubspacesoverBezoutdomain
3.3AffinegeometryoverBezoutdomain
3.4FundamentaltheoremsofaffinegeometryoverBezoutdomain
3.5Affinegeometryoverdivisionring
3.6ProjectivegeometryoverringswhichhaveIBN
Chapter4GeometryofRectangularMatricesoverBezoutDomains
4.1Geometryofrectangularmatricesoverdivisionring
4.2AffinegeometrystructuresofmaximalsetsonmatricesoverBezout
domain
4.3FundamentalTheoremofgeometryofrectangularmatricesover
Bezoutdomain
4.4Applicationsoffundamentaltheorem
4.5ProjectivegeometryofrectangularmatricesoverBezoutdomain
Chapter5GeometriesofHermitianandSkew-HermitianMatricesover
DivisionRing
5.1Maximalsetsofrank1ofHn(D)
5.2AdjacencypreservingbijectionsonHermitianmatrices
5.3Maximalsetsofrank2inHn(D)
5.4Affinegeometrystructuresofmaximalsetsofrank2inH2(D)
5.5Geometryof2~2Hermitianmatricesoverdivisionring
5.6Fundamentaltheoremofgeometryofnxn(n>3)Hermitian
matrices
5.7Geometryofskew-Hermitianmatricesoverdivisionring
5.8Applicationstoalgebra
5.9ProjectivegeometryofHermitianandsymmetricmatrices
Chapter6GeometryofSymmetricMatricesoverCommutativePID
6.1Arithmeticdistanceanddistanceonsymmetricmatrices
6.2Maximalsetsofrankoneandtwo
6.3Adjacencyandinvertibilityofdeterminantdivisorspreserving
maps
6.4Fundamentaltheoremofgeometryofsymmetricmatricesover
commutativePID
Chapter7GeometryofBlockTriangularMatricesoverDivisionRing
7.1Introduction
7.2Affinegeometrystructuresonmaximalsets
7.3Adjacencypreservingbijectivemapsonblocktriangularmatrices
7.4Fundamentaltheoremofgeometryofblocktriangularmatrices
7.5ApplicationsofFundamentalTheorem
Chapter8GeometryofMatricesoverSemisimpleRing
8.1Geometryofblockdiagonalmatricesoversomedivisionrings
8.2Geometryofrectangularmatricesoversemisimplering
8.3GeometryofblocktriangularmatricesoversimpleArtinianring
Reference
Index