The minimal power of the radical contained in the ideal

Question

Let $A$ be a Noetherian commutative ring. For an ideal $I\subseteq A$, there is some $n\in\Bbb N$ with $(\sqrt I)^n\subseteq I$.

Does the minimal $n$ with this property have a name? Has it been studied?

Answer 1

The closest thing I can think of is that one would say that "$\sqrt{I}/I$ has index of nilpotency $n$ in $R/I$".

I'm not aware of a more special term for what you're describing.

Maybe a logical extension would be to say $\sqrt{I}$ has $I$-potency index $n$".