Produit tensoriel.

Abstract

The tensor product is very useful and widely used in both Mathematics and Physics. We define it here in a very general framework, that of modules on a commutative ring, When the ring is a field we find all the linear algebra of vector space. When the ring is the ring of integers we find the whole theory of abelian groups. Following Bourbaki, We show how to construct the tensor product of two modules. We illustrate its use through the xample of quantum teleportation which uses complex finite-dimensional vector spaces equipped with a Hermitian scalar product (Hilbert spaces).