Exercise 6.3ΒΆ

The ring \(\mathbb{Z}_8\) is commutative, so our only option to show that it is not an integral domain is to show that it has a zero-divisor. There are in fact three zero-divisors in \(\mathbb{Z}_8\): they are \(\overline{2}, \overline{4},\) and \(\overline{6}\). Each of these yields \(\overline{0}\) when multiplied by \(\overline{4}\).