  We consider the superfluid-insulator transition for cold bosons under an
effective magnetic field. We investigate how the applied magnetic field affects
the Mott transition within mean field theory and find that the critical hopping
strength $(t/U)_c$, increases with the applied field. The increase in the
critical hopping follows the bandwidth of the Hofstadter butterfly at the given
value of the magnetic field. We also calculate the magnetization and superfluid
density within mean field theory.
