# 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 $I$:

$\map {\operatorname {Rad} } I := \set {a \in A: \exists n \in \N : a^n \in I}$