# Restklassenringe (Z)/2357/Operationstafeln

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### Operationstafeln für den Körper mit zwei Elementen

Der Restklassenkörper ${\displaystyle {}\mathbb {Z} /(2)=\{0,1\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {}+}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$
${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$
${\displaystyle {}1}$ ${\displaystyle {}1}$ ${\displaystyle {}0}$

${\displaystyle {}\cdot }$ ${\displaystyle {}0}$ ${\displaystyle {}1}$
${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$
${\displaystyle {}1}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$

### Operationstafeln für den Körper mit drei Elementen

Der Restklassenkörper ${\displaystyle {}\mathbb {Z} /(3)=\{0,1,2\}}$ hat die folgenden Operationstafeln (Verknüpfungstabellen):

${\displaystyle {\begin{array}{c||c|c|c|}+&0&1&2\\\hline 0&0&1&2\\1&1&2&0\\2&2&0&1\\\end{array}}}$

${\displaystyle {\begin{array}{c||c|c|c|}\cdot &0&1&2\\\hline 0&0&0&0\\1&0&1&2\\2&0&2&1\\\end{array}}}$

### Operationstafeln für den Körper mit fünf Elementen

Der Restklassenkörper ${\displaystyle {}\mathbb {Z} /(5)=\{0,1,2,3,4\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {\begin{array}{c||c|c|c|c|c|}+&0&1&2&3&4\\\hline 0&0&1&2&3&4\\1&1&2&3&4&0\\2&2&3&4&0&1\\3&3&4&0&1&2\\4&4&0&1&2&3\\\end{array}}}$

${\displaystyle {}\cdot }$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$
${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$
${\displaystyle {}1}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$
${\displaystyle {}2}$ ${\displaystyle {}0}$ ${\displaystyle {}2}$ ${\displaystyle {}4}$ ${\displaystyle {}1}$ ${\displaystyle {}3}$
${\displaystyle {}3}$ ${\displaystyle {}0}$ ${\displaystyle {}3}$ ${\displaystyle {}1}$ ${\displaystyle {}4}$ ${\displaystyle {}2}$
${\displaystyle {}4}$ ${\displaystyle {}0}$ ${\displaystyle {}4}$ ${\displaystyle {}3}$ ${\displaystyle {}2}$ ${\displaystyle {}1}$

### Operationstafeln für den Körper mit sieben Elementen

Der Restklassenkörper ${\displaystyle {}\mathbb {Z} /(7)=\{0,1,2,3,4,5,6\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {}+}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$
${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$
${\displaystyle {}1}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$
${\displaystyle {}2}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$
${\displaystyle {}3}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$
${\displaystyle {}4}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$
${\displaystyle {}5}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$
${\displaystyle {}6}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$

${\displaystyle {}\cdot }$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$
${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$
${\displaystyle {}1}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$
${\displaystyle {}2}$ ${\displaystyle {}0}$ ${\displaystyle {}2}$ ${\displaystyle {}4}$ ${\displaystyle {}6}$ ${\displaystyle {}1}$ ${\displaystyle {}3}$ ${\displaystyle {}5}$
${\displaystyle {}3}$ ${\displaystyle {}0}$ ${\displaystyle {}3}$ ${\displaystyle {}6}$ ${\displaystyle {}2}$ ${\displaystyle {}5}$ ${\displaystyle {}1}$ ${\displaystyle {}4}$
${\displaystyle {}4}$ ${\displaystyle {}0}$ ${\displaystyle {}4}$ ${\displaystyle {}1}$ ${\displaystyle {}5}$ ${\displaystyle {}2}$ ${\displaystyle {}6}$ ${\displaystyle {}3}$
${\displaystyle {}5}$ ${\displaystyle {}0}$ ${\displaystyle {}5}$ ${\displaystyle {}3}$ ${\displaystyle {}1}$ ${\displaystyle {}6}$ ${\displaystyle {}4}$ ${\displaystyle {}2}$
${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}6}$ ${\displaystyle {}5}$ ${\displaystyle {}4}$ ${\displaystyle {}3}$ ${\displaystyle {}2}$ ${\displaystyle {}1}$