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 $\operatorname{Rad} \left({I}\right)$ or $\sqrt {I}$ is defined as:


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