Definition:Radical of Ideal of Ring

Definition
Let $$A$$ be a commutative ring with unity.

Let $$I$$ be an ideal of $$A$$.

Then the radical of $$I$$, usually written $$\text{Rad}(I)$$ or $$\sqrt{I}$$ is


 * $\text{Rad}(A)=\left\{a\in A:a^n\in I\text{ for some positive integer }n\right\}$.