  In a hot, dilute, magnetized accretion flow, the electron mean-free path can
be much greater than the Larmor radius, thus thermal conduction is anisotropic
and along magnetic field lines. In this case, if the temperature decreases
outward, the flow may be subject to a buoyancy instability (the magnetothermal
instability, or MTI). The MTI amplifies the magnetic field, and aligns field
lines with the radial direction. If the accretion flow is differentially
rotating, the magnetorotational instability (MRI) may also be present. Using
two-dimensional, time-dependent magnetohydrodynamic simulations, we investigate
the interaction between these two instabilities. We use global simulations that
span over two orders of magnitude in radius, centered on the region around the
Bondi radius where the infall time of gas is longer than the growth time of
both the MTI and MRI. Significant amplification of the magnetic field is
produced by both instabilities, although we find that the MTI primarily
amplifies the radial component, and the MRI primarily the toroidal component,
of the field, respectively. Most importantly, we find that if the MTI can
amplify the magnetic energy by a factor $F_t$, and the MRI by a factor $F_r$,
then when the MTI and MRI are both present, the magnetic energy can be
amplified by a factor of $F_t \cdot F_r$. We therefore conclude that
amplification of the magnetic energy by the MTI and MRI operates independently.
We also find that the MTI contributes to the transport of angular momentum,
because radial motions induced by the MTI increase the Maxwell (by amplifying
the magnetic field) and Reynolds stresses. Finally, we find that thermal
conduction decreases the slope of the radial temperature profile. The increased
temperature near the Bondi radius decreases the mass accretion rate.
