Wir rechnen mit den Zahlen ${\displaystyle {}0,1,2,{\text{viele}}\,\,(v)}$ nach den folgenden Verknüpfungstabellen.

${\displaystyle {}+}$	${\displaystyle {}0}$	${\displaystyle {}1}$	${\displaystyle {}2}$	${\displaystyle {}v}$
${\displaystyle {}0}$	${\displaystyle {}0}$	${\displaystyle {}1}$	${\displaystyle {}2}$	${\displaystyle {}v}$
${\displaystyle {}1}$	${\displaystyle {}1}$	${\displaystyle {}2}$	${\displaystyle {}v}$	${\displaystyle {}v}$
${\displaystyle {}2}$	${\displaystyle {}2}$	${\displaystyle {}v}$	${\displaystyle {}v}$	${\displaystyle {}v}$
${\displaystyle {}v}$	${\displaystyle {}v}$	${\displaystyle {}v}$	${\displaystyle {}v}$	${\displaystyle {}v}$

und

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

Zeige, dass es sich dabei um einen kommutativen Halbring handelt. Gilt für diesen die