We investigate the influence of radiative transport on the growth of the
magnetorotational instability (MRI) in accretion discs. A general dispersion relation
describing the growth of small disturbances on a homogeneous background shear flow is
provided. It includes compressibility and radiative effects in the flux-limited diffusion
approximation. All the effects of radiation transport can be subsumed into one single
parameter, an effective speed of sound. Radiative diffusion does not affect the region
where the MRI operates, but it alters the growth rates of the MRI either by increasing or
decreasing them. We report about corresponding numerical simulations, which are also used
for a first investigation of the non-linear stage of the MRI in gas-pressure dominated
accretion discs with radiation transport included.