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Abstract Algebra

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Cancellation in Rings: integers and integers mod m

ABSALG-JFYE2O

A ring $R$ is said to have the cancellation property if for any nonzero $x, y, z$ in $R$, if $xy = zy$, then necessarily $x = z$.

Which of the following does not have the cancellation property?

A

$\mathbb{Z}/2\mathbb{Z}$

B

$\mathbb{Z}/3\mathbb{Z}$

C

$\mathbb{Z}/4\mathbb{Z}$

D

$\mathbb{Z}$