Introduction and Review of the Tame Case

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


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.


Galois Group Number Field Group Ring Group Homomorphism Algebraic Integer 
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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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