Exercise 2, § 4

Let $A$ be an integrally closed Noetherian domain and $E, F$ two finitely generated $A$-modules. Suppose that $E$ is torsion-free, that $\mathrm{Hom}_A(E, F)$ is reflexive and that $\mathrm{Ext}_A^1(E, F) = 0$. Show then that $F$ is reflexive. (Prove first that $F$ is torsion-free; if $T = F^{**}/c_F(F)$, calculate $\mathrm{Ass}(\mathrm{Hom}_A(E, T))$ in two ways using the exact sequence:

and Chapter IV, § 1, no. 4, Proposition 10.)