Balanced Map
Tensor Products of Modules
Suppose
is a left -module and is a right -module. The tensor product of and over , denoted by , is an abelian group satisfying the following universal property: for any abelian group and any -balanced map , there exists a unique group homomorphism such that the following diagram commutes: In other words, it is the free module generated by
modulo the relations
, , , that make the map
bilinear.