| preface ListofS.vmbols Introduction ChapterⅠ Groups I.Groups,Subgroups,andHomomorphisms 2.PermutationGroups 3.TheSymmetricandAlternatingGroups 4.TheSylowTheorems 5.SolvableGroups,NormalandSubnormalSeries 6.Products 7.NiipotentGroups 8.FiniteAbelianGroups 9.FreeGroups 10.GeneratorsandRelations II.SomeFiniteGroupsClassified 12.FurtherExercises ChapterⅡ Rings 1.Preliminaries:IdealsandHomomorphisms 2.TheFieldofFractionsofanIntegralDomain 3.Polynomials 4.PolynomialsinSeveralIndeterminates 5.DivisibilityandFactorization 6.TheChineseRemainderTheorem 7.TheHilbcrtBasisTheorem 8.FurtherExercises ChapterⅢ FieldsandGaloisTheory 1.FieldExtensions 2.TheFundamentalTheoremofGaloisTheory 3.NormalityandSeparability 4.TheGaloisTheoryofEquations 5.SymmetricFunctions 6.GoametricalConstructions 7.NormandTrace 8.FurtherExercises ChapterⅣ Modules 1.Preliminaries 2.DirectSums,FreeModules 3.FinitelyGeneratedModulesoveraPID 4.ApplicationstoLinearAlgebra 5.Computations 6.TensorProducts 7.FurtherExercises ChapterⅤ StructureofRingsandAlgebras 1.Preliminaries 2.TheJacobsonRadical 3.TheDensityTheorem 4.ArtinianRings 5.FurtherExercises ChapterⅥ FurtherTopics 1.InfiniteAbelianGroups 2.P61ya-RedfieidEnumeration 3.PSL(V) 4.IntegralDependenceandDedekindDomains 5.TranscendentalFieldExtensions 6.Valuationsandp-adicNumbers 7.RealFieldsandSturm'sTheorem 8.RepresentationsandCharactersofFiniteGroups 9.SomeGaloisGroups AppendixZorn'sLemma References |
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