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2
of
'Chinese remainder theorem'
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| Title of object: |
Chinese remainder theorem |
| Canonical Name: |
ChineseRemainderTheorem2 |
| Type: |
Theorem |
| Created on: |
2002-02-03 01:43:37 |
| Modified on: |
2002-08-20 02:08:50 |
| Classification: |
msc:11N99, msc:11A05, msc:13A15 |
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 $R$ be a commutative ring with identity. If $a_1,\ldots,a_n$ are ideals of $R$ such that $a_i + a_j = R$ whenever $i\neq j$, then $\cap a_i = \prod a_i$ and
$\frac{R}{\prod a_i} = \prod \frac{R}{a_i}$ |
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