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The Theory of Algebraic Number Fields
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Abstract
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Individual chapters are listed in the "Chapters" tab
Suggested Citation
DOI: 10.1007/978-3-662-03545-0
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Book Chapters
The following chapters of this book are listed in IDEAS- David Hilbert, 1998. "Algebraic Numbers and Number Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 1, pages 3-7, Springer.
- David Hilbert, 1998. "Ideals of Number Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 2, pages 9-16, Springer.
- David Hilbert, 1998. "Congruences with Respect to Ideals," Springer Books, in: The Theory of Algebraic Number Fields, chapter 3, pages 17-23, Springer.
- David Hilbert, 1998. "The Discriminant of a Field and its Divisors," Springer Books, in: The Theory of Algebraic Number Fields, chapter 4, pages 25-32, Springer.
- David Hilbert, 1998. "Extension Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 5, pages 33-39, Springer.
- David Hilbert, 1998. "Units of a Field," Springer Books, in: The Theory of Algebraic Number Fields, chapter 6, pages 41-52, Springer.
- David Hilbert, 1998. "Ideal Classes of a Field," Springer Books, in: The Theory of Algebraic Number Fields, chapter 7, pages 53-64, Springer.
- David Hilbert, 1998. "Reducible Forms of a Field," Springer Books, in: The Theory of Algebraic Number Fields, chapter 8, pages 65-66, Springer.
- David Hilbert, 1998. "Orders in a Field," Springer Books, in: The Theory of Algebraic Number Fields, chapter 9, pages 67-75, Springer.
- David Hilbert, 1998. "Prime Ideals of a Galois Number Field and its Subfields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 10, pages 79-88, Springer.
- David Hilbert, 1998. "The Differents and Discriminants of a Galois Number Field and its Subfields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 11, pages 89-91, Springer.
- David Hilbert, 1998. "Connexion Between the Arithmetic and Algebraic Properties of a Galois Number Field," Springer Books, in: The Theory of Algebraic Number Fields, chapter 12, pages 93-96, Springer.
- David Hilbert, 1998. "Composition of Number Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 13, pages 97-99, Springer.
- David Hilbert, 1998. "The Prime Ideals of Degree 1 and the Class Concept," Springer Books, in: The Theory of Algebraic Number Fields, chapter 14, pages 101-103, Springer.
- David Hilbert, 1998. "Cyclic Extension Fields of Prime Degree," Springer Books, in: The Theory of Algebraic Number Fields, chapter 15, pages 105-111, Springer.
- David Hilbert, 1998. "Factorisation of Numbers in Quadratic Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 16, pages 115-119, Springer.
- David Hilbert, 1998. "Genera in Quadratic Fields and Their Character Sets," Springer Books, in: The Theory of Algebraic Number Fields, chapter 17, pages 121-132, Springer.
- David Hilbert, 1998. "Existence of Genera in Quadratic Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 18, pages 133-147, Springer.
- David Hilbert, 1998. "Determination of the Number of Ideal Classes of a Quadratic Field," Springer Books, in: The Theory of Algebraic Number Fields, chapter 19, pages 149-153, Springer.
- David Hilbert, 1998. "Orders and Modules of Quadratic Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 20, pages 155-157, Springer.
- David Hilbert, 1998. "The Roots of Unity with Prime Number Exponent l and the Cyclotomic Field They Generate," Springer Books, in: The Theory of Algebraic Number Fields, chapter 21, pages 161-165, Springer.
- David Hilbert, 1998. "The Roots of Unity for a Composite Exponent m and the Cyclotomic Field They Generate," Springer Books, in: The Theory of Algebraic Number Fields, chapter 22, pages 167-173, Springer.
- David Hilbert, 1998. "Cyclotomic Fields as Abelian Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 23, pages 175-185, Springer.
- David Hilbert, 1998. "The Root Numbers of the Cyclotomic Field of the l-th Roots of Unity," Springer Books, in: The Theory of Algebraic Number Fields, chapter 24, pages 187-197, Springer.
- David Hilbert, 1998. "The Reciprocity Law for l-th Power Residues Between a Rational Number and a Number in the Field of l-th Roots of Unity," Springer Books, in: The Theory of Algebraic Number Fields, chapter 25, pages 199-205, Springer.
- David Hilbert, 1998. "Determination of the Number of Ideal Classes in the Cyclotomic Field of the m-th Roots of Unity," Springer Books, in: The Theory of Algebraic Number Fields, chapter 26, pages 207-215, Springer.
- David Hilbert, 1998. "Applications of the Theory of Cyclotomic Fields to Quadratic Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 27, pages 217-222, Springer.
- David Hilbert, 1998. "Factorisation of the Numbers of the Cyclotomic Field in a Kummer Field," Springer Books, in: The Theory of Algebraic Number Fields, chapter 28, pages 225-232, Springer.
- David Hilbert, 1998. "Norm Residues and Non-residues of a Kummer Field," Springer Books, in: The Theory of Algebraic Number Fields, chapter 29, pages 233-251, Springer.
- David Hilbert, 1998. "Existence of Infinitely Many Prime Ideals with Prescribed Power Characters in a Kummer Field," Springer Books, in: The Theory of Algebraic Number Fields, chapter 30, pages 253-256, Springer.
- David Hilbert, 1998. "Regular Cyclotomic Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 31, pages 257-268, Springer.
- David Hilbert, 1998. "Ambig Ideal Classes and Genera in Regular Kummer Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 32, pages 269-288, Springer.
- David Hilbert, 1998. "The l-th Power Reciprocity Law in Regular Cyclotomic Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 33, pages 289-304, Springer.
- David Hilbert, 1998. "The Number of Genera in a Regular Kummer Field," Springer Books, in: The Theory of Algebraic Number Fields, chapter 34, pages 305-312, Springer.
- David Hilbert, 1998. "New Foundation of the Theory of Regular Kummer Fields," Springer Books, in: The Theory of Algebraic Number Fields, chapter 35, pages 313-326, Springer.
- David Hilbert, 1998. "The Diophantine Equation α m + β m + γ m = 0," Springer Books, in: The Theory of Algebraic Number Fields, chapter 36, pages 327-333, Springer.
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