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I believe that if we are given two modules $M,N$ over a ring $R$, and a pairing between them $M \otimes_R N \to R$, we can construct a perfect pairing $M'\otimes_R N' \to R$ by taking kernels.

Is there a name for this construction?

Thanks.

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associated perfect/non-degenerate pairing? –  slackenerny Oct 3 '10 at 17:44

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