Let $M$ be a noetherian module over noetherian ring $A$.
How to prove that there exists submodule $N\subset M$ such that $$M/N\cong A/\mathfrak{p}$$ for some prime ideal $\mathfrak{p}\in A$.
Is it true that any submodule of noetherian module over noetherian ring is noetherian? (because it is finitely generated as submodule of noetherian module?)
Thanks a lot!