Is it possible to have an infinitely generated reduction of a finitely generated ideal in a commutative ring with identity ? If yes, why ? If no, an example to this effect will be helpful.
Thank you.
Edit. By reduction, I meant the following: if $J$ and $I$ are ideals with $J \subset I$, then $J$ is a reduction of $I$ if there exists an integer $n$ such that $I^{n+1}=JI^n$.
