|
The concept of pairing treated here occurs in mathematics. ==Definition== Let ''R'' be a commutative ring with unity, and let ''M'', ''N'' and ''L'' be three ''R''-modules. A pairing is any ''R''-bilinear map . That is, it satisfies :, : and for any and any and 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. If a pairing is called alternating if for the above map we have . A pairing is called non-degenerate if for the above map we have that for all implies . 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「pairing」の詳細全文を読む スポンサード リンク
|