数学研究生教材：伽罗瓦理论

图书标准信息

• 作者 [美]爱德华滋 著
• 出版社 世界图书出版公司
• 出版时间 2010-09
• 版次 1
• ISBN 9787510027420
• 定价 29.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 152页
• 正文语种 英语

【内容简介】

ThisexpositionofGaloistheorywasoriginallygoingtobeChapterIofthecontinuationofmybookFerrnatsLastTheorem，butitsoonoutgrewanyreasonableboundsforanintroductorychapter，andIdecidedtomakeitaseparatebook.However，thisdecisionwaspromptedbymorethanjustthelength.Followingthepreceptsofmysermon"ReadtheMasters！"[E2]，ImadethereadingofGaloisoriginalmemoiramajorpartofmystudyofGaloistheory，andIsawthatthemoderntreatmentsofGaloistheorylackedmuchofthesimplicityandclarityoftheoriginal.ThereforeIwantedtowriteaboutthetheoryinawaythatwouldnotonlyexplainit，butexplainitintermscloseenoughtoGaloisowntomakehismemoiraccessibletothereader，inthesamewaythatItriedtomakeRiemannsmemoironthezetafunctionandKummerspapersonFermatsLastTheoremaccessibleinmyearlierbooks，[Eliand[E3].ClearlyIcouldnotdothiswithintheconfinesofoneexpositorychapter

【目录】

Acknowledgments
1.Galois2.InfluenceofLagrange3.Quadraticequations4.1700B.c.toA.D.15005.Solutionofcubic6.Solutionofquartic7.Impossibilityofquintic8.Newton9.Symmetricpolynomialsinroots10.Fundamentaltheoremonsymmetricpolynomials11.Proof12.Newtonstheorem13.Discriminants
FirstExerciseSet13
14.Solutionofcubic15.LagrangeandVandermonde16.Lagrangeresolvents17.Solutionofquarticagain18.Attemptatquintic19.LagrangesRdflexions
SecondExerciseSet22
20.Cyclotomicequations21.Thecasesn=3，522.n=7，1123.Generalcase24.Twolemmas25.Gausssmethod26.p-gonsbyrulerandcompass27.SummaryThirdExerciseSet31
28.Resolvents29.Lagrangestheorem30.Proof31.Galoisresolvents32.ExistenceofGaloisresolvents33.RepresentationofthesplittingfieldasK（t）34.Simplealgebraicextensions35.Euclideanalgorithm36.Constructionofsimplealgebraicextensions37.Galoismethod
FourthExerciseSet45
38.Review39.Finitepermutationgroups40.Subgroups，normalsubgroups41.TheGaloisgroupofanequation42.Examples
FifthExerciseSet56
3.Solvabilitybyradicals44.ReductionoftheGaloisgroupbyacyclicextension5.Solvablegroups46.Reductiontoanormalsubgroupofindexp47.Theoremonsolutionbyradicals（assumingrootsofunity）48.Summary
SixthExerciseSet65
49.Splittingfields50.Fundamentaltheoremofalgebra（so-called）51.
Constructionofasplittingfield52.Needforafactorizationmethod53.Threetheoremsonfactorizationmethods54.Uniquenessoffactorizationofpolynomials55.Factorizationover56.Over57.Gaussslemma，factorizationover58.Overtranscendentalextensions59.
Ofpolynomialsintwovariables60.Overalgebraicextensions61.Finalremarks
SeventhExerciseSet81
62.ReviewofGaloistheory63.FundamentaltheoremofGaloistheory（so-called）64.Galoisgroupofxp-1=0over65.Solvabilityofthecyclotomicequation6.Theoremonsolutionbyradicals67.Equationswithliteralcoefficients68.Equationsofprimedegree69.
Galoisgroupofxn-1=0over70.Proofofthemainproposition71.DeductionofLemma2of24
EighthExerciseSet97
Appendix1.MemoirontheConditionsforSolvabilityofEquationsbyRadicals，byEvaristeGalois
Appendix2.Synopsis
Appendix3.Groups
AnswerstoExercises
ListofExercises
References
Index