  We briefly report on our result that the braided tensor product algebra of
two module algebras $A_1,A_2$ of a quasitriangular Hopf algebra $H$ is equal to
the ordinary tensor product algebra of $H_1$ with a subalgebra isomorphic to
$A_2$ and commuting with $A_1$, provided there exists a realization of $H$
within $A_1$. As applications of the theorem we consider the braided tensor
product algebras of two or more quantum group covariant quantum spaces or
deformed Heisenberg algebras.
