Let $A$ be a <Noetherian ring> that is an <integral domain>. If
$$
0\longrightarrow M\longrightarrow N\longrightarrow P\longrightarrow0
$$
is <exact sequence>[exact], $N$ is a finitely generated <free module>, and $P$ is a <torsion-free module>, then $M$ is a <reflexive module>. In particular, the dual of every finitely generated $A$-module is reflexive.


Reflexive-module second-syzygy criterion

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A finitely generated module $M$ over a <commutative ring> $A$ is reflexive when its <evaluation homomorphism> $M\to M^{**}$ to the <double dual module> is an <isomorphism>.


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 Incoming links: Reflexive module