radical ideal

《Algebra》 · 第 409 页 · Chapter VI，Section 2，Definition 2.13

Let $I$ be an ideal in a commutative ring $R$. The radical of $I$ is the ideal $\sqrt I=\{r\in R\mid \exists k\geq 0,\ r^k\in I\}$. An ideal $I$ is a radical ideal if $\sqrt I=I$.