  We study the vacuum radiative corrections to energy levels of a confined
electron in quantum rings. The calculations are provided for the Lamb shift of
energy levels in low-momentum region of virtual photons and for both
one-dimensional and two-dimensional quantum rings. We show that contrary to the
well known case of a hydrogen atom the value of the Lamb shift increases with
the magnetic momentum quantum number m. We also investigate the dependence of
the Lamb shift on magnetic flux piercing the ring and demonstrate a presence of
magnetic-flux-dependent oscillations. For one-dimensional ring the value of the
shift strongly depends on the radius of the ring. It is extremely small for
semiconductor rings but can attain measurable quantities in natural organic
ring-shape molecules, such as benzene, cycloalcanes and porphyrins.
