Solution
= Solution
In the <polynomial ring> $\mathbb Z[x]$, the ideal $(x)$ is nonzero and prime: the <quotient ring> $\mathbb Z[x]/(x)$ is isomorphic to the <integral domain> $\mathbb Z$, by evaluation at zero. It is not maximal, since that quotient is not a <field>. Equivalently $(x)\subsetneq(2,x)\subsetneq\mathbb Z[x]$. Thus \b[$(x)$ is a nonzero prime ideal which is not maximal].