Lemma 15.23.8. Let $R$ be a Noetherian domain. Let $M$ be a finite $R$-module. Let $N$ be a finite reflexive $R$-module. Then $\mathop{\mathrm{Hom}}\nolimits _ R(M, N)$ is reflexive.

**Proof.**
Choose a presentation $R^{\oplus m} \to R^{\oplus n} \to M \to 0$. Then we obtain

\[ 0 \to \mathop{\mathrm{Hom}}\nolimits _ R(M, N) \to N^{\oplus n} \to N' \to 0 \]

with $N' = \mathop{\mathrm{Im}}(N^{\oplus n} \to N^{\oplus m})$ torsion free. We conclude by Lemma 15.23.5. $\square$

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