The Theory of Algebraic Number Fields

Hilbert, David

The Theory of Algebraic Number Fields

David Hilbert

in Springer Books from Springer

Date: 1998
ISBN: 978-3-662-03545-0
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Chapters in this book:

Ch 1 Algebraic Numbers and Number Fields: David Hilbert
Ch 2 Ideals of Number Fields: David Hilbert
Ch 3 Congruences with Respect to Ideals: David Hilbert
Ch 4 The Discriminant of a Field and its Divisors: David Hilbert
Ch 5 Extension Fields: David Hilbert
Ch 6 Units of a Field: David Hilbert
Ch 7 Ideal Classes of a Field: David Hilbert
Ch 8 Reducible Forms of a Field: David Hilbert
Ch 9 Orders in a Field: David Hilbert
Ch 10 Prime Ideals of a Galois Number Field and its Subfields: David Hilbert
Ch 11 The Differents and Discriminants of a Galois Number Field and its Subfields: David Hilbert
Ch 12 Connexion Between the Arithmetic and Algebraic Properties of a Galois Number Field: David Hilbert
Ch 13 Composition of Number Fields: David Hilbert
Ch 14 The Prime Ideals of Degree 1 and the Class Concept: David Hilbert
Ch 15 Cyclic Extension Fields of Prime Degree: David Hilbert
Ch 16 Factorisation of Numbers in Quadratic Fields: David Hilbert
Ch 17 Genera in Quadratic Fields and Their Character Sets: David Hilbert
Ch 18 Existence of Genera in Quadratic Fields: David Hilbert
Ch 19 Determination of the Number of Ideal Classes of a Quadratic Field: David Hilbert
Ch 20 Orders and Modules of Quadratic Fields: David Hilbert
Ch 21 The Roots of Unity with Prime Number Exponent l and the Cyclotomic Field They Generate: David Hilbert
Ch 22 The Roots of Unity for a Composite Exponent m and the Cyclotomic Field They Generate: David Hilbert
Ch 23 Cyclotomic Fields as Abelian Fields: David Hilbert
Ch 24 The Root Numbers of the Cyclotomic Field of the l-th Roots of Unity: David Hilbert
Ch 25 The Reciprocity Law for l-th Power Residues Between a Rational Number and a Number in the Field of l-th Roots of Unity: David Hilbert
Ch 26 Determination of the Number of Ideal Classes in the Cyclotomic Field of the m-th Roots of Unity: David Hilbert
Ch 27 Applications of the Theory of Cyclotomic Fields to Quadratic Fields: David Hilbert
Ch 28 Factorisation of the Numbers of the Cyclotomic Field in a Kummer Field: David Hilbert
Ch 29 Norm Residues and Non-residues of a Kummer Field: David Hilbert
Ch 30 Existence of Infinitely Many Prime Ideals with Prescribed Power Characters in a Kummer Field: David Hilbert
Ch 31 Regular Cyclotomic Fields: David Hilbert
Ch 32 Ambig Ideal Classes and Genera in Regular Kummer Fields: David Hilbert
Ch 33 The l-th Power Reciprocity Law in Regular Cyclotomic Fields: David Hilbert
Ch 34 The Number of Genera in a Regular Kummer Field: David Hilbert
Ch 35 New Foundation of the Theory of Regular Kummer Fields: David Hilbert
Ch 36 The Diophantine Equation α m + β m + γ m = 0: David Hilbert

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DOI: 10.1007/978-3-662-03545-0

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