nLab
archimedean valued field

Contents

Definition

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

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 January 9, 2012 06:09:09 by Toby Bartels (216.96.8.189)