\begin{definition}[Definition:Radical of Ideal of Ring/Definition 1]
Let $A$ be a commutative ring with unity.
Let $I$ be an ideal of $A$.
The '''radical of $I$''' is the ideal of elements of which some power is in $I$:
:$\map \Rad I := \set {a \in A: \exists n \in \N : a^n \in I}$
\end{definition}