Definition:Radical of Ideal of Ring

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

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

Also denoted as
The radical of $I$ is also denoted as $\sqrt I$ or $r \left({I}\right)$.

The notation $\sqrt I$ is not recommended, as it is to easy to conflate with the sign for the square root, and so will not be used on.

Also see

 * Equivalence of Definitions of Radical of Ideal of Ring
 * Definition:Radical Ideal of Ring
 * Radical of Ideal is Intersection of Containing Prime Ideals

Special cases

 * Definition:Radical of Integer
 * Definition:Nilradical of Ring, the radical of the zero ideal

Generalizations

 * Definition:Radical of Subset of Ring