|
|
|
Viewing Version
4
of
'independence of the valuations'
|
[ view 'independence of the valuations'
|
back to history
]
| Title of object: |
independence of the valuations |
| Canonical Name: |
IndependenceOfTheValuations |
| Type: |
Theorem |
| Created on: |
2004-02-25 17:59:09 |
| Modified on: |
2004-02-25 18:21:07 |
| Classification: |
msc:11R99 |
| Keywords: |
non-equivalent, valuation |
| Synonyms: |
independence of the valuations=approximation theorem |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
Let $|\cdot|_1$, . . . , $|\cdot|_n$ be non-trivial and pairwise non-equivalent valuations of a field $K$. If $a_1$, ..., $a_n$ are some elements of this field, and $\epsilon$ an arbitrary positive number, then there exists in $K$ an element $y$ which satisfies the conditions
$$|y-a_1|_1 < \epsilon,$$
$$.$$ $$.$$
$$|y-a_n|_n < \epsilon.$$ |
|
|
|
|
|
