Endlicher Körper/9/Operationstafeln

Wir nehmen die Darstellung

${𝔽}_9\cong {𝔽}_3[X]/(X^2+1)$.

Dabei ist $X^2+1$ irreduzibel in ${𝔽}_3[X]$, da es keine Nullstelle in ${𝔽}_3$ besitzt (da $-1$ kein Quadrat in ${𝔽}_3[X]$ ist). Es bezeichne $x$ die Restklasse von $X$.

$+$	$0$	$1$	$2$	$x$	$x+1$	$x+2$	$2x$	$2x+1$	$2x+2$
$0$	$0$	$1$	$2$	$x$	$x+1$	$x+2$	$2x$	$2x+1$	$2x+2$
$1$	$1$	$2$	$0$	$x+1$	$x+2$	$x$	$2x+1$	$2x+2$	$2x$
$2$	$2$	$0$	$1$	$x+2$	$x$	$x+1$	$2x+2$	$2x$	$2x+1$
$x$	$x$	$x+1$	$x+2$	$2x$	$2x+1$	$2x+2$	$0$	$1$	$2$
$x+1$	$x+1$	$x+2$	$x$	$2x+1$	$2x+2$	$2x$	$1$	$2$	$0$
$x+2$	$x+2$	$x$	$x+1$	$2x+2$	$2x$	$2x+1$	$2$	$0$	$1$
$2x$	$2x$	$2x+1$	$2x+2$	$0$	$1$	$2$	$x$	$x+1$	$x+2$
$2x+1$	$2x+1$	$2x+2$	$2x$	$1$	$2$	$0$	$x+1$	$x+2$	$x$
$2x+2$	$2x+2$	$2x$	$2x+1$	$2$	$0$	$1$	$x+2$	$x$	$x+1$

$\cdot$	$0$	$1$	$2$	$x$	$x+1$	$x+2$	$2x$	$2x+1$	$2x+2$
$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
$1$	$0$	$1$	$2$	$x$	$x+1$	$x+2$	$2x$	$2x+1$	$2x+2$
$2$	$0$	$2$	$1$	$2x$	$2x+2$	$2x+1$	$x$	$x+2$	$x+1$
$x$	$0$	$x$	$2x$	$2$	$x+2$	$2x+2$	$1$	$x+1$	$2x+1$
$x+1$	$0$	$x+1$	$2x+2$	$x+2$	$2x$	$1$	$2x+1$	$2$	$x$
$x+2$	$0$	$x+2$	$2x+1$	$2x+2$	$1$	$x$	$x+1$	$2x$	$2$
$2x$	$0$	$2x$	$x$	$1$	$2x+1$	$x+1$	$2$	$2x+2$	$x+2$
$2x+1$	$0$	$2x+1$	$x+2$	$x+1$	$2$	$2x$	$2x+2$	$x$	$1$
$2x+2$	$0$	$2x+2$	$x+1$	$2x+1$	$x$	$2$	$x+2$	$1$	$2x$