We show that the endomorphism algebra over an algebraically closed field of tensor product of two modules is the tensor product of their endomorphisms. We used that the tensor product of two indecomposable modules is indecomposable module. We investigate if the exterior tensor product of two Brauer indecomposable modules is a Brauer indecomposable module.

induction and restriction modules, relative trace maps, module theory, Brauer theory, tensor product.