Let $M$ be an (infinitely generated) free module over a ring $R$, with generating set(not basis) $\{\alpha\_i\}\_{i \in \Lambda}$ . Let $N$ be a finitely generated $R$-module such that $f: N \rightarrow M$ is an injective module homomorphism. Can we say that there are finitely many $\{\alpha\_i\}$ such that image of $N$ is contained in the submodule generated by them?