  The vertical shear instability (VSI) is a robust phenomenon in irradiated
protoplanetary disks (PPDs). While there is extensive literature on the VSI in
the hydrodynamic limit, PPDs are expected to be magnetized and their extremely
low ionization fractions imply that non-ideal magneto-hydrodynamic (MHD)
effects should be properly considered. To this end, we present linear analyses
of the VSI in magnetized disks with Ohmic resistivity. We primarily consider
toroidal magnetic fields, which are likely to dominate the field geometry in
PPDs. We perform vertically global and radially local analyses to capture
characteristic VSI modes with extended vertical structures. To focus on the
effect of magnetism, we use a locally isothermal equation of state. We find
that magnetism provides a stabilizing effect to dampen the VSI, with surface
modes, rather than body modes, being the first to vanish with increasing
magnetization. Subdued VSI modes can be revived by Ohmic resistivity, where
sufficient magnetic diffusion overcome magnetic stabilization, and hydrodynamic
results are recovered. We also briefly consider poloidal fields to account for
the magnetorotational instability (MRI), which may develop towards surface
layers in the outer parts of PPDs. The MRI grows efficiently at small radial
wavenumbers, in contrast to the VSI. When resistivity is considered, we find
the VSI dominates over the MRI for Ohmic Els\"{a}sser numbers $\lesssim 0.09$
at plasma beta parameter $\beta_Z \sim 10^4$.
