Let $A$ be a noetherian ring and $M$ a finite $A$-module. That is there exist $m_1,...m_k \in M$ which generate $M$ as $A$-module. Let $N \subset M$ a submodule of $M$. It's a well known fact that since $A$ noetherian every submodule of finite $A$-module is also finite.
Although I found plenty proofs like this one no one I found was constructive, that is no one contained a direct method to construct explicitely a set of generators $n_1,..., n_s$ of $N$ from $m_1,...m_k \in M$.
Question: Does there exist a constructive proof of quoted result containing a method to construct generators of $N$ explicitly?