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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

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Dual of finite reflexive modules

Let $A$ be a commutative ring and $M$ be a finite reflexive $A$-module, i.e. the natural map $M\to (M^{\vee})^{\vee}$ is an isomorphism. Can we deduce that the dual $M^{\vee}$ is also finite?
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