Let $R$ be an integrally closed local domain. Suppose there is a $y\in I^n$ such that $yI^n=I^{2n}$ for some $n$. I would like to prove that $I^n=(y)$.
Source: The above question comes from the proof of Lemma F on page 449 of this paper.
A proof is given, but i cannot understand it, I seem to be missing something very simple it seems.
I asked this question earlier and somebody downvoted, so i thought about it a little more, but still i feel i am missing something.