  In this paper we investigate the influence of radiative transport on the
growth of the magnetorotational instability (MRI) in accretion discs. The
analysis is performed by use of analytical and numerical means. We provide a
general dispersion relation together with the corresponding eigenfunctions
describing the growth rates of small disturbances on a homogeneous background
shear flow. The dispersion relation includes compressibility and radiative
effects in the flux-limited diffusion approximation. By introducing an
effective speed of sound, all the effects of radiation transport can be
subsumed into one single parameter. It can be shown that the growth rates of
the vertical modes -- which are the fastest growing ones -- are reduced by
radiative transport. For the case of non-vertical modes, the growth rates may
instead be enhanced. We quantify the effects of compressibility and radiative
diffusion on the growth rates for the gas-pressure dominated case. The
analytical discussion is supplemented by 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.
