Other Definitions
pairing (dict)
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PairingLet R be a commutative ring with unity, and let M and N be two R-modules. A pairing is any R-bilinear map . That is, it satisfies -
for any . Or equivalently, a pairing is an R-linear map -
where denotes the tensor product of M and N. A pairing can also be considered as an R-linear map , which matches the first definition by setting . A pairing is called perfect if the above map is an isomorphism of R-modules.
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