$I$ be a finitely generated ideal of $R$ such that $R/I$ is a Noetherian and $R$ is $I$-adically complete. Then $R$ is Noetherian

Question

Let $R$ be a commutative ring with unity and $I$ be a finitely generated ideal of $R$ such that $R/I$ is a Noetherian ring and $R$ is complete with the $I$-adic topology. Then how to show that $R$ is Noetherian ?

I have no clue about where to start. The only thing I can see is that $\cap_{n\ge 1} I^n=(0)$ since $R$ is $I$-adic complete.

Please help.

Answer 1

Follow the proof in https://stacks.math.columbia.edu/tag/05GH starting with "let $f_1, \ldots, f_t$ be generators of $I$."