内容

目次

Algebraic NumbersOrigins and FoundationsAlgebraic Numbers and Number FieldsDiscriminants, Norms, and TracesAlgebraic Integers and Integral BasesFactorization and DivisibilityApplications of Unique FactorizationApplications to Factoring Using Cubic IntegersArithmetic of Number FieldsQuadratic FieldsCyclotomic FieldsUnits in Number RingsGeometry of NumbersDirichlet's Unit TheoremApplication: The Number Field SieveIdeal TheoryProperties of IdealsPID's and UFD'sNorms of IdealsIdeal Classes-The Class GroupClass Numbers of Quadratic FieldsCyclotomic Fields and Kummer's Theorem--Bernoulli Numbers and Irregular PrimesCryptography in Quadratic FieldsIdeal Decomposition in Extension FieldsInertia, Ramification, and SplittingThe Different and DiscriminantGalois Theory and DecompositionThe Kronecker-Weber TheoremAn Application--Primality TestingReciprocity LawsCubic ReciprocityThe Biquadratic Reciprocity LawThe Stickelberger RelationThe Eisenstein Reciprocity LawElliptic Curves, Factoring, and PrimalityAppendicesGroups, Modules, Rings, Fields, and MatricesSequences and SeriesGalois Theory (An Introduction with Exercises)The Greek AlphabetLatin PhrasesSolutions to Odd-Numbered ExercisesBibliographList of SymbolsIndex (over 1,700 entries)