  In this paper, we analyze the linear stability of a stellar accretion disk,
having a stratified morphology. The study is performed in the framework of
ideal magneto-hydrodynamics and therefore it results in a characterization of
the linear unstable magneto-rotational modes. The peculiarity of the present
scenario consists of adopting the magnetic flux function as the basic dynamical
variable. Such a representation of the dynamics allows to make account of the
co-rotation theorem as a fundamental feature of the ideal plasma equilibrium,
evaluating its impact on the perturbation evolution too. According to the
Alfvenic nature of the Magneto-rotational instability, we consider an
incompressible plasma profile and perturbations propagating along the
background magnetic field. Furthermore, we develop a local perturbation
analysis, around fiducial coordinates of the background configuration and
dealing with very small scale of the linear dynamics in comparison to the
background inhomogeneity size. The main issue of the present study is that the
condition for the emergence of unstable modes is the same in the stratified
plasma disk, as in the case of a thin configuration. Such a feature is the
result of the cancelation of the vertical derivative of the disk angular
frequency from the dispersion relation, which implies that only the radial
profile of the differential rotation is responsible for the trigger of growing
modes.
