Lemma 15.23.2. Let $R$ be a domain and let $M$ be an $R$-module.

If $M$ is reflexive, then $M$ is torsion free.

If $M$ is finite, then $j : M \to \mathop{\mathrm{Hom}}\nolimits _ R(\mathop{\mathrm{Hom}}\nolimits _ R(M, R), R)$ is injective if and only if $M$ is torsion free

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