Definition:Radical of Ideal of Ring/Definition 1

Definition
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 $I$:
 * $\operatorname{Rad} \left({I}\right) := \left\{{a \in A: \exists n \in \N : a^n \in I }\right\}$

Also see

 * Equivalence of Definitions of Radical of Ideal of Ring