\begin{definition}[Definition:Nilradical of Ring/Definition 2]
Let $A$ be a commutative ring with unity.
Let $\Spec A$ denote the prime spectrum of $A$.
The '''nilradical''' of $A$ is:
:$\ds \Nil A = \bigcap_{\mathfrak p \mathop \in \Spec A} \mathfrak p$
That is, it is the intersection of all prime ideals of $A$.
\end{definition}