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The theory of classical valuations /

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In his studies of cyclotomic fields, in view of establishing his monumental theorem about Fermat's last theorem, Kummer introduced "local" methods. They are concerned with divisibility of "ideal numbers" of cyclotomic fields by lambda = 1 - psi where psi is a primitive p-th...

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Bibliographic Details
Main Author: Ribenboim, Paulo
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York : Springer, [1999]
Subjects:
Algebraic fields.
Valuation theory.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Absolute Values of Fields
  • Valuations of a Field
  • Polynomials and Henselian Valued Fields
  • Extensions of Valuations
  • Uniqueness of Extensions of Valuations and Poly-Complete Fields
  • Extensions of Valuations: Numerical Relations
  • Power Series and the Structure of Complete Valued Fields
  • Decomposition and Inertia Theory
  • Ramification Theory
  • Valuation Characterization of Dedekind Domains
  • Galois Groups of Algebraic Extensions of Infinite Degree
  • Ideals, Valuations and Divisors in Algebraic Extensions of Infinite Degree of the Field of Rational Numbers
  • A Glimpse on Krull Valuations.