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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 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.

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