While doing exercise 4 of Chapter 6 in Atiyah & Macdonald's Introduction to Commutative Algebra, I got stuck at this step:
I have shown that $R/I$ is a Noetherian $R$-module. Here $R$ is a commutative ring with $1$ and $I$ is some ideal of $R$. How can I (no pun intended) conclude from here that $R/I$ is a Noetherian $R/I$-module?
Well, in the exercise $I$ is actually the annihilator of $R$-module $M$, but the argument above probably works for all ideals $I$.