Dual number
= Dual number
{title2=$k[\varepsilon]/(\varepsilon^2)$}
The dual-number ring over a <field> $k$ consists of elements $a+b\varepsilon$ with $\varepsilon^2=0$. The element $\varepsilon$ is a nonzero <nilpotent element>; its ideal is the ring's only <prime ideal>. Hence its <affine scheme> has the same one-point topology as $\operatorname{Spec}k$ while its <structure sheaf> differs.