In this paper, we analyse 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 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 us to take account of the co-rotation theorem as a fundamental featureof the ideal plasma equilibrium and to evaluate its impact on the perturbation evolution. 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 deal with very small-scale linear dynamics in comparison to the background inhomogeneity size. The m