A First Graduate Course in Abstract Algebra (Hardcover)

PREFACEGROUPS (MOSTLY FINITE)Definitions, Examples, Elementary PropertiesSubgroups, Cyclic GroupsFactorization in ZFirst Problem SetIsomorphismSecond Problem SetHomomorphismsThird Problem SetNormal Subgroups and Factor GroupsFourth Problem SetSimple Groups and Composition SeriesFifth Problem SetSymmetric GroupsSixth Problem SetConjugacy Classes, p-Groups, Solvable GroupsSeventh Problem SetDirect ProductsEighth Problem SetSylow TheoremsNinth Problem SetThe Structure of Finite Abelien GroupsTenth Problem SetRINGS (MOSTLY DOMAINS)Definitions and Elementary PropertiesEleventh Problem SetHomomorphisms, Ideals, and Factors RingsTwelfth Problem SetPrincipal Ideal DomainsThirteenth Problem SetPolynomialsFourteenth Problem SetI[x] is a UFD*Fifteenth Problem SetEuclidean Domains*Sixteenth Problem SetMODULESElementary ConceptsSeventeenth Problem SetFree and Projective ModulesEighteenth Problem SetTensor ProductsNineteenth Problem SetFinitely Generated Modules Over a PIDTwentieth Problem SetA Structure TheoremTwenty-First Problem SetVECTOR SPACESDefinitions and GlossaryTime for a Little Set TheoryA Structure Theorem for Vector SpacesTwenty-Second Problem SetFinite Remarks on Finite Dimensional Vector SpacesTwenty-Third Problem SetMatrices and Systems of EquationsTwenty-Fourth Problem SetLinear Transformations and MatricesTwenty-Fifth Problem SetDeterminantsTwenty-Sixth Problem SetCharacteristic Values, Vectors, Basis ChangeTwenty-Seventh Problem SetCanonical FormsTwenty-Eighth Problem SetDual Spaces*Twenty-Ninth Problem SetInner Product Spaces*Thirtieth Problem SetLinear Functionals and Adjoints*Thirty-First Problem SetFIELDS AND GALOIS THEORYPreliminary ResultsThirty-Second Problem SetStraight Edge and Compass ConstructionThirty-Third Problem SetSplitting FieldsThirty-Fourth Problem SetThe Algebraic Closure of a Field*Thirty-Fifth Problem SetA Structure Theorem for Finite FieldsThirty-Sixth Problem SetThe Galois CorrespondenceThirty-Seventh Problem SetGalois Criterion for Radical SolvabilityThirty-Eighth Problem SetThe General Equation of Degree nThirty-Ninth Problem SetTOPICS IN NONCOMMUTATIVE RINGSIntroductionSimple ModelsFortieth Problem SetThe Jacobson RadicalForty-First Problem SetThe Jacobson Density TheoremSemisimple Artinian RingsForty-Second Problem SetStructure of Complex Group AlgebrasApplications to Finite GroupsForty-Third Problem SetGROUP EXTENSIONSIntroductionExact Sequences and ZG-ModulesForty-Fourth Problem SetSemidirect ProductsForty-Fifth Problem SetExtensions and Factor SetsForty-Sixth Problem SetSolution of the Extension ProblemForty-Seventh Problem SetTOPICS IN ABELIAN GROUPSDirect Sums and ProductsForty-Eighth Problem SetStructure Theorem for Divisible GroupsForty-Ninth Problem SetRank One Torsion-Free GroupsFiftieth Problem SetStructure of Completely Decomposable GroupsFifty-First Problem SetAlgebraically Compact GroupsFifty-Second Problem Set Structure of Algebraically Compact GroupsFifty-Third Problem SetStructure of Countable Torsion GroupsFifty-Fourth Problem SetREFERENCESINDEX