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Could you give me an example of a non-reflexive module isomorphic to its double dual?

I found an example here but I cannot understand it, do you have any simpler examples?

By this question we should only use not finitely generated modules.

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In general I hope we don't get a lot of questions of the form "I didn't understand the solution to this other question. Give me easier solutions," but this one in particular seems like it can stand. – rschwieb Oct 8 '14 at 13:15

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