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[美]亨格福德 著 / 世界图书出版公司 / 2006-10 / 平装
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上书时间2021-03-17
代数
《代数》是Springer《数学研究生教材》第73卷,初版于1974年,30年来一直是美国及世界各国人学数学系采用的研究生代数教本。此书Springer已重印12次,由此证明这是一部经典的研究生教材。全书取材适中,论述清晰,自成体系。《代数》在一些问题的处理上有其独到之处,如sylow定理的证明、伽罗瓦理论的处理、可分域的扩张,环的结构理论等。书中有大量的练习和精心挑选的例子。
PrefaceAcknowledgmentsSuggestionsontheUseofThisBookIntroduction:PrerequisitesandPreliminaries1.Logic2.SetsandClasses3.Functions4.RelationsandPartitions5.Products6.TheIntegers7.TheAxiomofChoice,OrderandZornsLemma8.CardinalNumbersChapterI:Groups1.Semigroups,MonoidsandGroups2.HomomorphismsandSubgroups3.Cyclic.Groups4.CosetsandCounting5.Normality,QuotientGroups,andHomomorphisms6.Symmetric,Alternating,andDihedralGroups7.Categories:Products,Coproducts,andFreeObjects8.DirectProductsandDirectSums9,FreeGroups,FreeProducts,Generators&RelationsChapterII:TheStructureofGroups1.FreeAbelianGroups2.FinitelyGeneratedAbelianGroups3.TheKrull-SchmidtTheorem4.TheActionofaGrouponaSet5.TheSylowTheorems6.ClassificationofFiniteGroups7.NilpotentandSolvableGroups8.NormalandSubnormalSeriesChapterIll:Rings1.RingsandHomomorphisms2.Ideals3.FactorizationinCommutativeRings4.RingsofQuotientsandLocalization5.RingsofPolynomialsandFormalPowerSeries6.FactorizationinPolynomialRingsChapterIV:Modules1.Modules,HomomorphismsandExactSequences2.FreeModulesandVectorSpaces3.ProjectiveandInjectiveModules4.HomandDuality5.TensorProducts6.ModulesoveraPrincipalIdealDomain7.Algebras.ChapterV:FieldsandGaloisTheory1.FieldExtensionsAppendix:RulerandCompassConstructions2.TheFundamentalTheoremAppendix:SymmetricRationalFunctions3.SplittingFields,AlgebraicClosureandNormalityAppendix:TheFundamentalTheoremofAlgebra..4.TheGaloisGroupofaPolynomial5.FiniteFields6.Separability:7.CyclicExtensions8.CyclotomicExtensions9.RadicalExtensionsAppendix:TheGeneralEquationofDegreenChapterVI:TheStructureofFieldsChapterVII:LinearAlgebraChapterVIII:CommutativeRingsandModulesChapterIX:TheStructureofRingsChapterX:CategoriesListofSymbolsBibliographyIndex
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