抽象代数讲义 第3卷

presentVrolumecompletestheseriesoftextsonalgebrawhichtheauthorbeganmorethantenyearsago.TheaccountoffieldtheoryandGaloistheorywhichwegirrehereisbasedonthenotionsandresultsofgeneralalgebrawhichappearinourfirstvolumeandonthemoreelementarypartsofthesecondvolume，dealingwithlinearalgebra.Thelevelofthepresentwork.isroughlythesameasthatofVolumeII.目录INTRODUCTIONSECTION1.Extensionofhomomorphisms2.Algebras3.Tensorproductsofvectorspaces4.TensorproductofalgebrasCHAPTERIFINITEDIMENSIONALEXTENSIONFIELDS1Somevectorspacesassociatedwithmappingsoffields2.TheJacobson-Bourbakicorrespondence3.Dedekindindependencetheoremforisomorphismsofafield4.Finitegroupsofautomorphisms.5.Splittingfieldofapolynomial6.Multipleroots.Separablepolynomials7.The"fundamentaltheorem"ofGaloistheoryINTRODUCTIONSECTION1.Extensionofhomomorphisms2.Algebras3.Tensorproductsofvectorspaces4.TensorproductofalgebrasCHAPTERIFINITEDIMENSIONALEXTENSIONFIELDS1Somevectorspacesassociatedwithmappingsoffields2.TheJacobson-Bourbakicorrespondence3.Dedekindindependencetheoremforisomorphismsofafield4.Finitegroupsofautomorphisms.5.Splittingfieldofapolynomial6.Multipleroots.Separablepolynomials7.The"fundamentaltheorem"ofGaloistheory8.Normalextensions.Normalclosures9.Structureofalgebraicextensions.Separability10.Degreesofseparabilityandinseparability.Structureofnormalextensions11.Primitiveelements12.Normalbases13.Finitefields14.Regularrepresentation