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For questions on modules over rings.
5
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Accepted
Nondegenerate pairings versus perfect pairings for finitely generated projective modules
No: for $R=\mathbb{Z}$ and even for $M,N$ both free (i.e. free Abelian groups), non-degenerate doesn't imply perfect. (You get finite index sublattices, so torsion quotients, unlike the case of vector …