Operationstafeln für Z/(1)

Der Restklassenring ${\displaystyle \mathbb {Z} /(1)=\{0\}}$, genannt der Nullring, also 0 = 1, hat die folgenden Verknüpfungstabellen:

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

${\displaystyle {\begin{array}{c||c|c|c|}*&0\\\hline 0&0\\\end{array}}}$

Operationstafeln für Z/(2)

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 Z/(3)

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 Z/(4)

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

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

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

Operationstafeln für Z/(5)

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 Z/(6)

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

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|}+&0&1&2&3&4&5\\\hline 0&0&1&2&3&4&5\\1&1&2&3&4&5&0\\2&2&3&4&5&0&1\\3&3&4&5&0&1&2\\4&4&5&0&1&2&3\\5&5&0&1&2&3&4\\\end{array}}}$

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|}*&0&1&2&3&4&5\\\hline 0&0&0&0&0&0&0\\1&0&1&2&3&4&5\\2&0&2&4&0&2&4\\3&0&3&0&3&0&3\\4&0&4&2&0&4&2\\5&0&5&4&3&2&1\\\end{array}}}$

Operationstafeln für Z/(7)

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

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

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

Operationstafeln für Z/(8)

Der Restklassenring ${\displaystyle \mathbb {Z} /(8)=\{0,1,2,3,4,5,6,7\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|}+&0&1&2&3&4&5&6&7\\\hline 0&0&1&2&3&4&5&6&7\\1&1&2&3&4&5&6&7&0\\2&2&3&4&5&6&7&0&1\\3&3&4&5&6&7&0&1&2\\4&4&5&6&7&0&1&2&3\\5&5&6&7&0&1&2&3&4\\6&6&7&0&1&2&3&4&5\\7&7&0&1&2&3&4&5&6\\\end{array}}}$

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|}\cdot &0&1&2&3&4&5&6&7\\\hline 0&0&0&0&0&0&0&0&0\\1&0&1&2&3&4&5&6&7\\2&0&2&4&6&0&2&4&6\\3&0&3&6&1&4&7&2&5\\4&0&4&0&4&0&4&0&4\\5&0&5&2&7&4&1&6&3\\6&0&6&4&2&0&6&4&2\\7&0&7&6&5&4&3&2&1\\\end{array}}}$

Operationstafeln für Z/(9)

Der Restklassenring ${\displaystyle \mathbb {Z} /(9)=\{0,1,2,3,4,5,6,7,8\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|}+&0&1&2&3&4&5&6&7&8\\\hline 0&0&1&2&3&4&5&6&7&8\\1&1&2&3&4&5&6&7&8&0\\2&2&3&4&5&6&7&8&0&1\\3&3&4&5&6&7&8&0&1&2\\4&4&5&6&7&8&0&1&2&3\\5&5&6&7&8&0&1&2&3&4\\6&6&7&8&0&1&2&3&4&5\\7&7&8&0&1&2&3&4&5&6\\8&8&0&1&2&3&4&5&6&7\\\end{array}}}$

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|}*&0&1&2&3&4&5&6&7&8\\\hline 0&0&0&0&0&0&0&0&0&0\\1&0&1&2&3&4&5&6&7&8\\2&0&2&4&6&8&1&3&5&7\\3&0&3&6&0&3&6&0&3&6\\4&0&4&8&3&7&2&6&1&5\\5&0&5&1&6&2&7&3&8&4\\6&0&6&3&0&6&3&0&6&3\\7&0&7&5&3&1&8&6&4&2\\8&0&8&7&6&5&4&3&2&1\\\end{array}}}$

Operationstafeln für Z/(10)

Der Restklassenring ${\displaystyle \mathbb {Z} /(10)=\{0,1,2,3,4,5,6,7,8,9\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|}+&0&1&2&3&4&5&6&7&8&9\\\hline 0&0&1&2&3&4&5&6&7&8&9\\1&1&2&3&4&5&6&7&8&9&0\\2&2&3&4&5&6&7&8&9&0&1\\3&3&4&5&6&7&8&9&0&1&2\\4&4&5&6&7&8&9&0&1&2&3\\5&5&6&7&8&9&0&1&2&3&4\\6&6&7&8&9&0&1&2&3&4&5\\7&7&8&9&0&1&2&3&4&5&6\\8&8&9&0&1&2&3&4&5&6&7\\9&9&0&1&2&3&4&5&6&7&8\\\end{array}}}$

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|}*&0&1&2&3&4&5&6&7&8&9\\\hline 0&0&0&0&0&0&0&0&0&0&0\\1&0&1&2&3&4&5&6&7&8&9\\2&0&2&4&6&8&0&2&4&6&8\\3&0&3&6&9&2&5&8&1&4&7\\4&0&4&8&2&6&0&4&8&2&6\\5&0&5&0&5&0&5&0&5&0&5\\6&0&6&2&8&4&0&6&2&8&4\\7&0&7&4&1&8&5&2&9&6&3\\8&0&8&6&4&2&0&8&6&4&2\\9&0&9&8&7&6&5&4&3&2&1\\\end{array}}}$

Operationstafeln für Z/(11)

Der Restklassenring ${\displaystyle \mathbb {Z} /(11)=\{0,1,2,3,4,5,6,7,8,9,10\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|c|}+&0&1&2&3&4&5&6&7&8&9&10\\\hline 0&0&1&2&3&4&5&6&7&8&9&10\\1&1&2&3&4&5&6&7&8&9&10&0\\2&2&3&4&5&6&7&8&9&10&0&1\\3&3&4&5&6&7&8&9&10&0&1&2\\4&4&5&6&7&8&9&10&0&1&2&3\\5&5&6&7&8&9&10&0&1&2&3&4\\6&6&7&8&9&10&0&1&2&3&4&5\\7&7&8&9&10&0&1&2&3&4&5&6\\8&8&5&10&0&1&2&3&4&5&6&7\\9&9&10&0&1&2&3&4&5&6&7&8\\10&10&0&1&2&3&4&5&6&7&8&9\\\end{array}}}$

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|c|}*&0&1&2&3&4&5&6&7&8&9&10\\\hline 0&0&0&0&0&0&0&0&0&0&0&0\\1&0&1&2&3&4&5&6&7&8&9&10\\2&0&2&4&6&8&10&1&3&5&7&9\\3&0&3&6&9&1&4&7&10&2&5&8\\4&0&4&8&1&5&9&2&6&10&3&7\\5&0&5&10&4&9&3&8&2&7&1&6\\6&0&6&1&7&2&8&3&9&4&10&5\\7&0&7&3&10&6&2&9&5&1&8&4\\8&0&8&5&2&10&7&4&1&9&6&3\\9&0&9&7&5&3&1&10&8&6&4&2\\10&0&10&9&8&7&6&5&4&3&2&1\\\end{array}}}$

Operationstafeln für Z/(12)

Der Restklassenring ${\displaystyle \mathbb {Z} /(12)=\{0,1,2,3,4,5,6,7,8,9,10,11\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|c|c|}+&0&1&2&3&4&5&6&7&8&9&10&11\\\hline 0&0&1&2&3&4&5&6&7&8&9&10&11\\1&1&2&3&4&5&6&7&8&9&10&11&0\\2&2&3&4&5&6&7&8&9&10&11&0&1\\3&3&4&5&6&7&8&9&10&11&0&1&2\\4&4&5&6&7&8&9&10&11&0&1&2&3\\5&5&6&7&8&9&10&11&0&1&2&3&4\\6&6&7&8&9&10&11&0&1&2&3&4&5\\7&7&8&9&10&11&0&1&2&3&4&5&6\\8&8&9&10&11&0&1&2&3&4&5&6&7\\9&9&10&11&0&1&2&3&4&5&6&7&8\\10&10&11&0&1&2&3&4&5&6&7&8&9\\11&11&0&1&2&3&4&5&6&7&8&9&10\\\end{array}}}$

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|c|c|}*&0&1&2&3&4&5&6&7&8&9&10&11\\\hline 0&0&0&0&0&0&0&0&0&0&0&0&0\\1&0&1&2&3&4&5&6&7&8&9&10&11\\2&0&2&4&6&8&10&0&2&4&6&8&10\\3&0&3&6&9&0&3&6&9&0&3&6&9\\4&0&4&8&0&4&8&0&4&8&0&4&8\\5&0&5&10&3&8&1&6&11&4&9&2&7\\6&0&6&0&6&0&6&0&6&0&6&0&6\\7&0&7&2&9&4&11&6&1&8&3&10&5\\8&0&8&4&0&8&4&0&8&4&0&8&4\\9&0&9&6&3&0&9&6&3&0&9&6&3\\10&0&10&8&6&4&2&0&10&8&6&4&2\\11&0&11&10&9&8&7&6&5&4&3&2&1\\\end{array}}}$

Operationstafeln für Z/(13)

Der Restklassenring ${\displaystyle \mathbb {Z} /(13)=\{0,1,2,3,4,5,6,7,8,9,10,11,12\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|c|c|c|}+&0&1&2&3&4&5&6&7&8&9&10&11&12\\\hline 0&0&1&2&3&4&5&6&7&8&9&10&11&12\\1&1&2&3&4&5&6&7&8&9&10&11&12&0\\2&2&3&4&5&6&7&8&9&10&11&12&0&1\\3&3&4&5&6&7&8&9&10&11&12&0&1&2\\4&4&5&6&7&8&9&10&11&12&0&1&2&3\\5&5&6&7&8&9&10&11&12&0&1&2&3&4\\6&6&7&8&9&10&11&12&0&1&2&3&4&5\\7&7&8&9&10&11&12&0&1&2&3&4&5&6\\8&8&9&10&11&12&0&1&2&3&4&5&6&7\\9&9&10&11&12&0&1&2&3&4&5&6&7&8\\10&10&11&12&0&1&2&3&4&5&6&7&8&9\\11&11&12&0&1&2&3&4&5&6&7&8&9&10\\12&12&0&1&2&3&4&5&6&7&8&9&10&11\\\end{array}}}$

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|c|c|c|}*&0&1&2&3&4&5&6&7&8&9&10&11&12\\\hline 0&0&0&0&0&0&0&0&0&0&0&0&0&0\\1&0&1&2&3&4&5&6&7&8&9&10&11&12\\2&0&2&4&6&8&10&12&1&3&5&7&9&11\\3&0&3&6&9&12&2&5&8&11&1&4&7&10\\4&0&4&8&12&3&7&11&2&6&10&1&5&9\\5&0&5&10&2&7&12&4&9&1&6&11&3&8\\6&0&6&12&5&11&4&10&3&9&2&8&1&7\\7&0&7&1&8&2&9&3&10&4&11&5&12&6\\8&0&8&3&11&6&1&9&4&12&7&2&10&5\\9&0&9&5&1&10&6&2&11&7&3&12&8&4\\10&0&10&7&4&1&11&8&5&2&12&9&6&3\\11&0&11&9&7&5&3&1&12&10&8&6&4&2\\12&0&12&11&10&9&8&7&6&5&4&3&2&1\\\end{array}}}$

Operationstafeln für Z/(14)

Der Restklassenring ${\displaystyle \mathbb {Z} /(14)=\{0,1,2,3,4,5,6,7,8,9,10,11,12,13\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|c|c|c|c|}+&0&1&2&3&4&5&6&7&8&9&10&11&12&13\\\hline 0&0&1&2&3&4&5&6&7&8&9&10&11&12&13\\1&1&2&3&4&5&6&7&8&9&10&11&12&13&0\\2&2&3&4&5&6&7&8&9&10&11&12&13&0&1\\3&3&4&5&6&7&8&9&10&11&12&13&0&1&2\\4&4&5&6&7&8&9&10&11&12&13&0&1&2&3\\5&5&6&7&8&9&10&11&12&13&0&1&2&3&4\\6&6&7&8&9&10&11&12&13&0&1&2&3&4&5\\7&7&8&9&10&11&12&13&0&1&2&3&4&5&6\\8&8&9&10&11&12&13&0&1&2&3&4&5&6&7\\9&9&10&11&12&13&0&1&2&3&4&5&6&7&8\\10&10&11&12&13&0&1&2&3&4&5&6&7&8&9\\11&11&12&13&0&1&2&3&4&5&6&7&8&9&10\\12&12&13&0&1&2&3&4&5&6&7&8&9&10&11\\13&13&0&1&2&3&4&5&6&7&8&9&10&11&12\\\end{array}}}$

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\cdot &0&1&2&3&4&5&6&7&8&9&10&11&12&13\\\hline 0&0&0&0&0&0&0&0&0&0&0&0&0&0&0\\1&0&1&2&3&4&5&6&7&8&9&10&11&12&13\\2&0&2&4&6&8&10&12&0&2&4&6&8&10&12\\3&0&3&6&9&12&1&4&7&10&13&2&5&8&11\\4&0&4&8&12&2&6&10&0&4&8&12&2&6&10\\5&0&5&10&1&6&11&2&7&12&3&8&13&4&9\\6&0&6&12&4&10&2&8&0&6&12&4&10&2&8\\7&0&7&0&7&0&7&0&7&0&7&0&7&0&7\\8&0&8&2&10&4&12&6&0&8&2&10&4&12&6\\9&0&9&4&13&8&3&12&7&2&11&6&1&10&5\\10&0&10&6&2&12&8&4&0&10&6&2&12&8&4\\11&0&11&8&5&2&13&10&7&4&1&12&9&6&3\\12&0&12&10&8&6&4&2&0&12&10&8&6&4&2\\13&0&13&12&11&10&9&8&7&6&5&4&3&2&1\\\end{array}}}$

Operationstafeln für Z/(15)

Der Restklassenring ${\displaystyle \mathbb {Z} /(15)=\{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {\begin{array}{c||c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}+&0&1&2&3&4&5&6&7&8&9&10&11&12&13&14\\\hline 0&0&1&2&3&4&5&6&7&8&9&10&11&12&13&14\\1&1&2&3&4&5&6&7&8&9&10&11&12&13&14&0\\2&2&3&4&5&6&7&8&9&10&11&12&13&14&0&1\\3&3&4&5&6&7&8&9&10&11&12&13&14&0&1&2\\4&4&5&6&7&8&9&10&11&12&13&14&0&1&2&3\\5&5&6&7&8&9&10&11&12&13&14&0&1&2&3&4\\6&6&7&8&9&10&11&12&13&14&0&1&2&3&4&5\\7&7&8&9&10&11&12&13&14&0&1&2&3&4&5&6\\8&8&9&10&11&12&13&14&0&1&2&3&4&5&6&7\\9&9&10&11&12&13&14&0&1&2&3&4&5&6&7&8\\10&10&11&12&13&14&0&1&2&3&4&5&6&7&8&9\\11&11&12&13&14&0&1&2&3&4&5&6&7&8&9&10\\12&12&13&14&0&1&2&3&4&5&6&7&8&9&10&11\\13&13&14&0&1&2&3&4&5&6&7&8&9&10&11&12\\14&14&0&1&2&3&4&5&6&7&8&9&10&11&12&13\\\end{array}}}$