26.HomomorphismsandFactorRings89 27.PrimeandMaximalIdeals94 28.Gr¨obnerBasesforIdeals99 iii VI.ExtensionFields 29.IntroductiontoExtensionFields103 30.VectorSpaces107 31.AlgebraicExtensions111 32.GeometricConstructions115 33.FiniteFields116 VII.AdvancedGroupTheory 34.IsomorphismTheorems117 35.SeriesofGroups11...
proof rends to see what he or she wants to see however the instructor should fi nd this manual adequate for the purpose for which it is intended morgan vermontj b f july 2002 i contents 0 sets and relations1 i groups and subgroups 1 introduction and examples4 2 binary operations7 3 ...
49.TheIsomorphismExtensionTheorem164 50.SplittingFields165 51.SeparableExtensions167 52.TotallyInseparableExtensions171 53.GaloisTheory173 54.IllustrationsofGaloisTheory176 55.CyclotomicExtensions183 56.InsolvabilityoftheQuintic185 APPENDIXMatrixAlgebra187
49.TheIsomorphismExtensionTheorem164 50.SplittingFields165 51.SeparableExtensions167 52.TotallyInseparableExtensions171 53.GaloisTheory173 54.IllustrationsofGaloisTheory176 55.CyclotomicExtensions183 56.InsolvabilityoftheQuintic185 APPENDIXMatrixAlgebra187