Let \(R\) be a commutative ring and \(I\subseteq R\) an ideal. The radical of \(I\) is \[ \rad{I} \coloneqq \theset{r\in R\suchthat r^n\in I\text{ for some } n\geq 0}. \] The ideal \(I\) is radical if \(\rad{I} = I\).
Radical of an ideal
D-JLCOX
D-JLCOX
Let \(R\) be a commutative ring and \(I\subseteq R\) an ideal. The radical of \(I\) is \[ \rad{I} \coloneqq \theset{r\in R\suchthat r^n\in I\text{ for some } n\geq 0}. \] The ideal \(I\) is radical if \(\rad{I} = I\).