  Resistivity and viscosity have a significant role in establishing the energy
levels in turbulence driven by the magnetorotational instability (MRI) in local
astrophysical disk models. This study uses the Athena code to characterize the
effects of a constant shear viscosity \nu and Ohmic resistivity \eta in
unstratified shearing box simulations with a net toroidal magnetic flux. A
previous study of shearing boxes with zero net magnetic field performed with
the ZEUS code found that turbulence dies out for values of the magnetic Prandtl
number, P_m = \nu/\eta, below P_m \sim 1; for P_m \gtrsim 1, time- and
volume-averaged stress levels increase with P_m. We repeat these experiments
with Athena and obtain consistent results. Next, the influence of viscosity and
resistivity on the toroidal field MRI is investigated both for linear growth
and for fully-developed turbulence. In the linear regime, a sufficiently large
\nu or \eta can prevent MRI growth; P_m itself has little direct influence on
growth from linear perturbations. By applying a range of values for \nu and
\eta to an initial state consisting of fully developed turbulence in the
presence of a background toroidal field, we investigate their effects in the
fully nonlinear system. Here, increased viscosity enhances the turbulence, and
the turbulence decays only if the resistivity is above a critical value;
turbulence can be sustained even when P_m < 1, in contrast to the zero net
field model. While we find preliminary evidence that the stress converges to a
small range of values when \nu and \eta become small enough, the influence of
dissipation terms on MRI-driven turbulence for relatively large \eta and \nu is
significant, independent of field geometry.
