nLab
archimedean valued field

Context

Algebra

Analytic geometry

Contents

Definition

A (complete) archimedean valued field is a field equipped with an archimedean absolute value (and complete with respect to it).

A non-archimedean field is one that is not, hence one whose norm satisfies the ultrametric triangle inequality.

Properties

One of Ostrowski's theorems says that for kk a field complete with respect to an absolute value ||{\vert - \vert} either the absolute value is archimedean, in which case kk is either the field of real numbers or of complex numbers, or the absolute value is non-archimedean.

Revised on July 17, 2014 14:55:01 by Urs Schreiber (82.136.246.44)