  We present global 2D and 3D simulations of self-gravitating magnetized tori.
We used the 2D calculations to demonstrate that the properties of the MRI are
not affected by the presence of self-gravity: MHD turbulence and enhanced
angular momentum transport follow the linear growth of the instability. In 3D,
we have studied the interaction between an $m=2$ gravitational instability and
MHD turbulence. We found its strength to be significantly decreased by the
presence of the latter, showing that both instabilities strongly interact in
their non-linear phases. We discuss the consequences of these results.
