  Linear and nonlinear optical absorption coefficients of the two-dimensional
semiconductor ring in the perpendicular magnetic field $\bf B$ are calculated
within independent electron approximation. Characteristic feature of the energy
spectrum are crossings of the levels with adjacent nonpositive magnetic quantum
numbers as the intensity $B$ changes. It is shown that the absorption
coefficient of the associated optical transition is drastically decreased at
the fields corresponding to the crossing. Proposed model of the Volcano disc
allows to get simple mathematical analytical results, which provide clear
physical interpretation. An interplay between positive linear and
intensity-dependent negative cubic absorption coefficients is discussed; in
particular, critical light intensity at which additional resonances appear in
the total absorption dependence on the light frequency, is calculated as a
function of the magnetic field and levels' broadening.
