Tensor product

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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 .


The tensor product of two -modules and , denoted by , is an -module satisfying the universal property


The functor is right-exact from the category of (right) to the category of -modules.

The derived functors .

Tensor products in linear algebra