Tensor product: Difference between revisions
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imported>Giovanni Antonio DiMatteo |
imported>Giovanni Antonio DiMatteo |
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==Definition== | ==Definition== | ||
The ''tensor product'' of two <math>R</math>-modules <math>M</math> and <math>M'</math>, denoted by <math>M\otimes_R M'</math>, is an <math>R | The ''tensor product'' of two <math>R</math>-modules <math>M</math> and <math>M'</math>, denoted by <math>M\otimes_R M'</math>, is an <math>R</math>-module <math>T</math> satisfying the universal property | ||
==Functoriality== | ==Functoriality== | ||
Revision as of 17:27, 9 December 2007
The tensor product is a bifunctor in the category of modules over a fixed ring . In the subcategory of algebras over , the tensor product is just the cofibered product over .
Definition
The tensor product of two -modules and , denoted by , is an -module satisfying the universal property
