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Introduction and Review of the Tame Case

  • Klaus W. Roggenkamp
  • Martin J. Taylor
Chapter
Part of the DMV Seminar book series (OWS, volume 18)

Abstract

The motivation behind the material presented in these notes is the following question:- if N/K is a finite Galois extension of number fields with Galois group Γ, and if \( mathfrak{D}{\text{ and }}\mathfrak{D}N \) are the rings of algebraic integers in K and N respectively, then what can be said about \( mathfrak{D}N \) as a Γ-module? A complete answer to this would be a description of \( mathfrak{D}N \) as a module over the group ring \( mathfrak{D}\Gamma \) , but since in general \( mathfrak{D}N \) need not be free over \( mathfrak{D} \) , it is more fruitful to restrict scalars and view \( mathfrak{D}N \) as a ℤΓ-module.

Keywords

Galois Group Number Field Group Ring Group Homomorphism Algebraic Integer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1992

Authors and Affiliations

  • Klaus W. Roggenkamp
    • 1
  • Martin J. Taylor
    • 2
  1. 1.Mathematisches Institut BUniversität StuttgartStuttgart 80Germany
  2. 2.Dept. of Mathematics U.M.I.S.T.ManchesterEngland

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