近世代数概论

图书标准信息

• 作者 [美]伯克霍夫（Birkhoff,G.）、[美]麦克莱恩（MacLane,S） 著
• 出版社 人民邮电出版社
• 出版时间 2007-08
• 版次 1
• ISBN 9787115162311
• 定价 69.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 496页
• 字数 612千字
• 正文语种 英语
• 原版书名 A Survey of Modern Algebra
• 丛书 图灵原版数学·统计学系列

【内容简介】

《近世代数概论（英文版）（第5版）》出自近世代数领域的两位科学巨匠之手，是一本经典的教材。全书共分为15章，内容包括：整数、多项式、实数、复数、矩阵代数、线性群、行列式和标准型、布尔代数和格、超限算术、环和理想、代数数域和伽罗华理论等。
《近世代数概论（英文版）（第5版）》曾帮助过几代人理解近世代数，至今仍是一本非常有价值的参考书和教材，适合数学专业及其他理工科专业高年级本科生和研究生使用。

【作者简介】

GarettBirkhoff（1911-1996）已故世界著名数学家，生前曾任国际数学家大会组织委员会主席、美国数学会副主席，美国工业与应用数学会主席、《大不列颠百科全书》编委，美国科学院院士，哈佛大学教授，1933年开创格论研究，使其成为数学的一个重要分文。

【目录】

PrefacetotheFourthEdition
1TheIntegers
1.1CommutativeRings;IntegralDomains
1.2ElementaryPropertiesofCommutativeRings
1.3OrderedDomains
1.4Well-OrderingPrinciple
1.5FiniteInduction;LawsofExponents
1.6ivisibility
1.7TheEuclideanAlgorithm
1.8FundamentalTheoremofArithmetic
1.9Congruences
1.10TheRingsZn
1.11Sets,Functions,andRelations
1.12IsomorphismsandAutomorphisms
2RationalNumbersandFields
2.1DefinitionofaField
2.2ConstructionoftheRationals
2.3SimultaneousLinearEquations
2.4OrderedFields
2.5PostulatesforthePositiveIntegers
2.6PeanoPostulates
3Polynomials
3.1PolynomialForms
3.2PolynomialFunctions
3.3HomomorphismsofCommutativeRings
3.4PolynomialsinSeveralVariables
3.5TheDivisionAlgorithm
3.6UnitsandAssociates
3.7IrreduciblePolynomials
3.8UniqueFactorizationTheorem
3.9OtherDomainswithUniqueFactorization
3.10EisensteinsIrreducibilityCriterion
3.11PartialFractions
4RealNumbers
4.1DilemmaofPythagoras
4.2UpperandLowerBounds
4.3PostulatesforRealNumbers
4.4RootsofPolynomialEquations
4.5DedekindCuts
5ComplexNumbers
5.1Definition
5.2TheComplexPlane
5.3FundamentalTheoremofAlgebra
5.4ConjugateNumbersandRealPolynomials
5.5QuadraticandCubicEquations
5.6SolutionofQuarticbyRadicals
5.7EquationsofStableType
6Groups
6.1SymmetriesoftheSquare
6.2GroupsofTransformations
6.3FurtherExamples
6.4AbstractGroups
6.5Isomorphism
6.6CyclicGroups
6.7Subgroups143
6.8LagrangesTheorem
6.9PermutationGroups
6.10EvenandOddPermutations
6.11Homomorphisms
6.12Automorphisms;ConjugateElements
6.13QuotientGroups
6.14EquivalenceandCongruenceRelations
7VectorsandVectorSpaces
7.1VectorsinaPlane
7.2Generalizations
7.3VectorSpacesandSubspaces
7.4LinearIndependenceandDimension
7.5MatricesandRow-equivalence
7.6TestsforLinearDependence
7.7VectorEquations;HomogeneousEquations
7.8BasesandCoordinateSystems
7.9InnerProducts
7.10EuclideanVectorSpaces
7.11NormalOrthogonalBases
7.12Quotient-spaces
7.13LinearFunctionsandDualSpaces
8TheAlgebraofMatrices
8.1LinearTransformationsandMatrices
8.2MatrixAddition
8.3MatrixMultiplication
8.4Diagonal,Permutation,andTriangularMatrices
8.5RectangularMatrices
8.6Inverses
8.7RankandNullity
8.8ElementaryMatrices243
8.9EquivalenceandCanonicalForm
8.10BilinearFunctionsandTensorProducts
8.11Quaternions
9LinearGroups
9.1ChangeofBasis
9.2SimilarMatricesandEigenvectors
9.3TheFullLinearandAffineGroups
9.4TheOrthogonalandEuclideanGroups
9.5InvariantsandCanonicalForms
9.6LinearandBilinearForms
9.7QuadraticForms
9.8QuadraticFormsUndertheFullLinearGroup
9.9RealQuadraticFormsUndertheFullLinearGroup
9.10QuadraticFormsUndertheOrthogonalGroup
9.11QuadricsUndertheAffineandEuclideanGroups
9.12UnitaryandHermitianMatrices
9.13AffineGeometry
9.14ProjectiveGeometry
10DeterminantsandCanonicalForms
10.1DefinitionandElementaryPropertiesofDeterminants
10.2ProductsofDeterminants
10.3DeterminantsasVolumes
10.4TheCharacteristicPolynomial
10.5TheMinimalPolynomial
10.6Cayley-HamiltonTheorem
10.7InvariantSubspacesandReducibility
10.8FirstDecompositionTheorem
10.9SecondDecompositionTheorem
10.10RationalandJordanCanonicalForms
11BooleanAlgebrasandLattices
11.1BasicDefinition
11.2Laws:AnalogywithArithmetic
11.3BooleanAlgebra
11.4DeductionofOtherBasicLaws
11.5CanonicalFormsofBooleanPolynomials
11.6PartialOrderings
11.7Lattices
11.8RepresentationbySets
12TransfiniteArithmetic
12.1NumbersandSets
12.2CountableSets
12.3OtherCardinalNumbers
12.4AdditionandMultiplicationofCardinals
12.5Exponentiation
13RingsandIdeals
13.1Rings
13.2Homomorphisms
13.3Quotient-rings
13.4AlgebraofIdeals
13.5PolynomialIdeals
13.6IdealsinLinearAlgebras
13.7TheCharacteristicofaRing
13.8CharacteristicsofFields
14AlgebraicNumberFields
14.1AlgebraicandTranscendentalExtensions
14.2ElementsAlgebraicoveraField
14.3AdjunctionofRoots
14.4DegreesandFiniteExtensions
14.5IteratedAlgebraicExtensions
14.6AlgebraicNumbers
14.7GaussianIntegers
14.8AlgebraicIntegers
14.9SumsandProductsofIntegers
14.10FactorizationofQuadraticIntegers
15GaloisTheory
15.1RootFieldsforEquations
15.2UniquenessTheorem
15.3FiniteFields
15.4TheGaloisGroup
15.5SeparableandInseparablePolynomials
15.6PropertiesoftheGaloisGroup
15.7SubgroupsandSubfields
15.8IrreducibleCubicEquations
15.9InsolvabilityofQuinticEquations
Bibliography
ListofSpecialSymbols
Index489