Restklassenringe (Z)/2357/Operationstafeln

Operationstafeln für den Körper mit zwei Elementen

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

${}+$	${}0$	${}1$
${}0$	${}0$	${}1$
${}1$	${}1$	${}0$

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

Operationstafeln für den Körper mit drei Elementen

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

${}+$	${}0$	${}1$	${}2$
${}0$	${}0$	${}1$	${}2$
${}1$	${}1$	${}2$	${}0$
${}2$	${}2$	${}0$	${}1$

${}\cdot$	${}0$	${}1$	${}2$
${}0$	${}0$	${}0$	${}0$
${}1$	${}0$	${}1$	${}2$
${}2$	${}0$	${}2$	${}1$

Operationstafeln für den Körper mit fünf Elementen

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

${}+$	${}0$	${}1$	${}2$	${}3$	${}4$
${}0$	${}0$	${}1$	${}2$	${}3$	${}4$
${}1$	${}1$	${}2$	${}3$	${}4$	${}0$
${}2$	${}2$	${}3$	${}4$	${}0$	${}1$
${}3$	${}3$	${}4$	${}0$	${}1$	${}2$
${}4$	${}4$	${}0$	${}1$	${}2$	${}3$

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

Operationstafeln für den Körper mit sieben Elementen

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

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

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