Let $A$ be a ring $M$ an $A$-module and $N$ a submodule. Definition: $N$ is called a pure submodule of $M$ if the sequence $0 \rightarrow N \otimes E \rightarrow M \otimes E$ is exact for every $A$-module $E$.
Since exactness commutes with inductive limits and since every module is the inductive limit of finitely generated submodules, then it is enough for a submodule $N$ to be pure, that the above sequence is exact for every finitely generated module $E$.
Question: Matsumura in his Commutative Ring Theory p. 53 comments that it is enough to restrict attention to finitely presented modules $E$. Since the set of finitely presented modules is a proper subset of the set of finitely generated modules over $A$, why is Matsumura's statement valid?