Complete Fields

  • Jean-Pierre Serre
Part of the Lecture Notes in Mathematics book series (LNM, volume 1500)

Abstract

Let k be a commutative field. An absolute value on k is a function k → R+ denoted by x ↦ |x|, xk satisfying the conditions:
  1. 1.

    |x| = 0 ⇔ x = 0.

     
  2. 2.

    |xy| = |x||y|.

     
  3. 3.

    |1| = 1.

     
  4. 4.

    |x + y| ≤ |x| + |y|.

     

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

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

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