The Stacks project

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

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

  2. 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

Comments (1)

Comment #9796 by Laurent Moret-Bailly on

I would also include (somewhere) the fact that if is finite, has torsion kernel and cokernel because is an isomorphism. (This is inspired by comment #9794).

There are also:

  • 1 comment(s) on Section 15.23: Reflexive modules

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