Radiatively inefficient accretion flows onto black holes are unstable due to both an outwardly decreasing entropy ('convection') and an outwardly decreasing rotation rate (the 'magnetorotational instability'; MRI). Using a linear magnetohydrodynamic stability analysis, we show that long-wavelength modes are primarily destabilized by the entropy gradient and that such 'convective' modes transport angular momentum inwards. Moreover, the stability criteria for the convective modes are the standard

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... Hoiland criteria of hydrodynamics. By contrast, shorter wavelength modes are primarily destabilized by magnetic tension and differential rotation. These 'MRI' modes transport angular momentum outwards. The convection-dominated accretion flow (CDAF) model, which has been proposed for radiatively inefficient accretion onto a black hole, posits that inward angular momentum transport and outward energy transport by long-wavelength convective fluctuations are crucial for determining the structure of the accretion flow. Our analysis suggests that the CDAF model is applicable to a magnetohydrodynamic accretion flow provided the magnetic field saturates at a sufficiently sub-equipartition value (plasma beta >> 1), so that long-wavelength convective fluctuations can fit inside the accretion disk. Numerical magnetohydrodynamic simulations are required to determine whether such a sub-equipartition field is in fact obtained.