代数

作者: [美] 亨格福德著

出版社: 世界图书出版公司

出版时间: 2006-10

版次: 1

ISBN: 9787506282291

定价: 49.00

装帧: 平装

开本: 其他

纸张: 胶版纸

页数: 502页

正文语种: 简体中文，英语

分类: 教材教辅考试>教材>研究生教材>工程技术

　　《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。 Preface
Acknowledgments
SuggestionsontheUseofThisBook
Introduction：PrerequisitesandPreliminaries
1.Logic
2.SetsandClasses
3.Functions
4.RelationsandPartitions
5.Products
6.TheIntegers
7.TheAxiomofChoice，OrderandZornsLemma
8.CardinalNumbers

ChapterI：Groups
1.Semigroups，MonoidsandGroups
2.HomomorphismsandSubgroups
3.Cyclic.Groups
4.CosetsandCounting
5.Normality，QuotientGroups，andHomomorphisms
6.Symmetric，Alternating，andDihedralGroups
7.Categories：Products，Coproducts，andFreeObjects
8.DirectProductsandDirectSums
9，FreeGroups，FreeProducts，Generators&Relations

ChapterII：TheStructureofGroups
1.FreeAbelianGroups
2.FinitelyGeneratedAbelianGroups
3.TheKrull-SchmidtTheorem
4.TheActionofaGrouponaSet
5.TheSylowTheorems
6.ClassificationofFiniteGroups
7.NilpotentandSolvableGroups
8.NormalandSubnormalSeries

ChapterIll：Rings
1.RingsandHomomorphisms
2.Ideals
3.FactorizationinCommutativeRings
4.RingsofQuotientsandLocalization
5.RingsofPolynomialsandFormalPowerSeries
6.FactorizationinPolynomialRings

ChapterIV：Modules
1.Modules，HomomorphismsandExactSequences
2.FreeModulesandVectorSpaces
3.ProjectiveandInjectiveModules
4.HomandDuality
5.TensorProducts
6.ModulesoveraPrincipalIdealDomain
7.Algebras.

ChapterV：FieldsandGaloisTheory
1.FieldExtensions
Appendix：RulerandCompassConstructions
2.TheFundamentalTheorem
Appendix：SymmetricRationalFunctions
3.SplittingFields，AlgebraicClosureandNormality
Appendix：TheFundamentalTheoremofAlgebra..
4.TheGaloisGroupofaPolynomial
5.FiniteFields
6.Separability：
7.CyclicExtensions
8.CyclotomicExtensions
9.RadicalExtensions
Appendix：TheGeneralEquationofDegreen
ChapterVI：TheStructureofFields
ChapterVII：LinearAlgebra

ChapterVIII：CommutativeRingsandModules
ChapterIX：TheStructureofRings
ChapterX：Categories
ListofSymbols
Bibliography
Index
内容简介:
　　《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。
目录:
Preface
Acknowledgments
SuggestionsontheUseofThisBook
Introduction：PrerequisitesandPreliminaries
1.Logic
2.SetsandClasses
3.Functions
4.RelationsandPartitions
5.Products
6.TheIntegers
7.TheAxiomofChoice，OrderandZornsLemma
8.CardinalNumbers

ChapterI：Groups
1.Semigroups，MonoidsandGroups
2.HomomorphismsandSubgroups
3.Cyclic.Groups
4.CosetsandCounting
5.Normality，QuotientGroups，andHomomorphisms
6.Symmetric，Alternating，andDihedralGroups
7.Categories：Products，Coproducts，andFreeObjects
8.DirectProductsandDirectSums
9，FreeGroups，FreeProducts，Generators&Relations

ChapterII：TheStructureofGroups
1.FreeAbelianGroups
2.FinitelyGeneratedAbelianGroups
3.TheKrull-SchmidtTheorem
4.TheActionofaGrouponaSet
5.TheSylowTheorems
6.ClassificationofFiniteGroups
7.NilpotentandSolvableGroups
8.NormalandSubnormalSeries

ChapterIll：Rings
1.RingsandHomomorphisms
2.Ideals
3.FactorizationinCommutativeRings
4.RingsofQuotientsandLocalization
5.RingsofPolynomialsandFormalPowerSeries
6.FactorizationinPolynomialRings

ChapterIV：Modules
1.Modules，HomomorphismsandExactSequences
2.FreeModulesandVectorSpaces
3.ProjectiveandInjectiveModules
4.HomandDuality
5.TensorProducts
6.ModulesoveraPrincipalIdealDomain
7.Algebras.

ChapterV：FieldsandGaloisTheory
1.FieldExtensions
Appendix：RulerandCompassConstructions
2.TheFundamentalTheorem
Appendix：SymmetricRationalFunctions
3.SplittingFields，AlgebraicClosureandNormality
Appendix：TheFundamentalTheoremofAlgebra..
4.TheGaloisGroupofaPolynomial
5.FiniteFields
6.Separability：
7.CyclicExtensions
8.CyclotomicExtensions
9.RadicalExtensions
Appendix：TheGeneralEquationofDegreen
ChapterVI：TheStructureofFields
ChapterVII：LinearAlgebra

ChapterVIII：CommutativeRingsandModules
ChapterIX：TheStructureofRings
ChapterX：Categories
ListofSymbols
Bibliography
Index

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代数

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