Observations suggest the existence of both hot and cold matter in the
centers of active galactic nuclei. Recent spectral models require a ma
jor fraction of power to be dissipated in the hot matter. We study the
case when the hot matter forms a corona around a standard cold alpha-
disk. In particular, we investigate the case when a major fraction, f,
of the power released when the cold matter accretes is transported to
and dissipated in the corona. This has major effects on the cold disk
, making it colder, more geometrically thin, denser, and having larger
optical depths. One important consequence is the disappearance of the
effectively optically thin zone as well as of the radiation pressure
dominated zone for values off sufficiently closed to unity. The disapp
earance of the radiation pressure dominated zone will result in a cold
disk with only a gas pressure dominated zone that is stable against t
hermal and viscous instabilities. We also show that the pressure (and
the radiation) from the corona will only affect the surface layers of
the cold disk. Our results disagree with those of other recent work on
accretion disks with coronae. We find those works to be based on unph
ysical assumptions.