# Kommutativer Halbring/1,2,viele/Aufgabe

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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

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