  The transport of angular momentum (AM) and chemical elements within evolving
stars remains poorly understood. Recent observations showed that the radiative
cores of low mass main sequence stars and red giants rotate orders of magnitude
slower than classical stellar evolution models predictions and that their
surface light elements abundances are too small. Magnetohydrodynamic (MHD)
turbulence can enhance the transport in radiative stellar interiors but its
efficiency is still largely uncertain. Here we explore the transport of AM and
chemical elements due to azimuthal magnetorotational instability (AMRI) using
3D MHD direct numerical simulations in a spherical shell. First, we provide
evidence of AMRI in the parameter regime expected from local and global linear
stability studies and then we analyze its nonlinear evolution. For unstratified
flow, we observe AMRI-driven dynamo action at values of the magnetic Prandtl
number Pm in the range $0.6-1$, the smallest ever reported in a global setup.
When considering stable stratification (under the Boussinesq approximation) at
$\text{Pm}=1$, the turbulence is instead transitional and becomes less
homogeneous and isotropic upon increasing buoyancy effects. We find that the
transport of AM occurs radially outwards and is dominated by the Maxwell
stresses when stratification is large enough. The associated turbulent
viscosity decreases when buoyancy effects strengthen and scales with the square
root of the ratio of the rotation rate to the Brunt-V\"ais\"al\"a frequency,
predicting that, for example, red giant cores may reach a state of uniform
rotation in a few thousand years. A passive scalar allows us to study the
transport of chemical elements. The chemical turbulent diffusion coefficient
scales with stratification similarly to the turbulent viscosity but is lower in
amplitude as suggested by recent stellar evolution models of low mass stars.
