Discrete Valuation Rings and Dedekind Domains

  • Jean-Pierre Serre
Part of the Graduate Texts in Mathematics book series (GTM, volume 67)


A ring A is called a discrete valuation ring if it is a principal ideal domain (Bourbaki, Alg., Chap. VII) that has a unique non-zero prime ideal m(A). [Recall that an ideal p of a commutative ring A is called prime if the quotient ring A/p is an integral domain.]


Prime Ideal Local Ring Maximal Ideal Galois Group Galois Extension 


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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Collège de FranceParisFrance

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