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1、353117NOTREDAMEMATHEMATICALLECTURESNumber2GALOISTHEORYLecturesdeliveredattheUniversityofNotreDamebyDR.EMILARTINProfessorofMathematics,PrincetonUniversityEditedandsupplementedwithaSectiononApplicationsbyDR.ARTHURN.MILGRAMAssociateProfessorofMathematics,UniversityofMinnesotaSecondEditionWithAdditionsa
2、ndRevisionsUNIVERSITYOFNOTREDAMEPRESSNOTREDAMELONDONCopyright1942,1944UNIVERSITYOFNOTREDAMESecondPrinting,February1964ThirdPrinting,July1965FourthPrinting,August1966NewcompositionwithcorrectionsFifthPrinting,March1970SixthPrinting,January1971PrintedintheUnitedStatesofAmericabyNAPCOGraphieArts,Inc.,M
3、ilwaukee,WisconsinTABLEOFCONTENTS(Thesectionsmarkedwithanasteriskhavebeenhereinaddedtothecontentofthefirstedition)Page1LINEARALGEBRA....................................1A.Fields...........................................1B.VectorSpaces....................................1C.HomogeneousLinearEquations
4、.....................2D.DependenceandIndependenceofVectors..,.........4E.Non-homogeneousLinearEquations.................9F.*Determinants.....................................11IIFIELDTHEORY.............................<.........21A.ExtensionFields.................................21B.Polynomials......
5、................................22C.AlgebraicElements...............................25D.SplittingFields...................................30E.UniqueDecompositionofPolynomialsintoIrreducibleFactors...........,..........33F.GroupCharacters.................................34G.*ApplicationsandExamplesto
6、Theorem13............38H.NormalExtensions................................41FiniteFields....................................49J.RootsofUnity.................................,..56K.NoetherEquations................................57L.Kummer’sFields..................................59M.SimpleExtensions.
7、...............................64N.ExistenceofaNormalBasis...........,...........66Q.TheoremonNaturalIrrationalities...................67111APPLICATIONSByA.N.Milgram.,.....................,...........
