archimedean valued field

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

One of Ostrowski's theorems says that for $k$ a field complete with respect to an absolute value ${\vert - \vert}$ either the absolute value is archimedean, in which case $k$ 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)