  The study of the magnetic field in stellar radiation zones is an important
topic in modern astrophysics because the magnetic field can play an important
role in several transport phenomena such as mixing and angular momentum
transport. We consider the influence of rotation on stability of a
predominantly toroidal magnetic field in the radiation zone. We find that the
effect of rotation on the stability depends on the magnetic configuration of
the basic state. If the toroidal field increases sufficiently rapidly with the
spherical radius, the instability cannot be suppressed entirely even by a very
fast rotation although the strength of the instability can be significantly
reduced. On the other hand, if the field increases slowly enough with the
radius or decreases, the instability has a threshold and can be completely
suppressed in rapidly rotating stars. We find that in the regions where the
instability is entirely suppressed a particular type of magnetohydrodynamic
waves may exist which are marginally stable.
