next up previous
Next: tensor products and localizations Up: tensor products and inverse Previous: universality of tensor products

additional structures on tensor products

LEMMA 3.4   Let $ A$ be a (not necessarily commutative) ring. Let $ M$ be a right $ A$ -module. Let $ N$ be a left $ A$ -module. If $ M$ carries a structure of an $ A$ -algebra, then the tensor product $ M\times_A N$ carries a structure of $ M$ -module in the following manner.

$\displaystyle x. (y\otimes n )= (xy) \otimes n \qquad (x,y\in M, n \in N)
$



2007-12-11