  A simple algebraic model for charged particle moving in two dimensional space
under influence of singular magnetic field is given. The fundamental assumption
for the model is that every charged particle coupled to the magnetic field is
transformed into a system of quasiparticles. It is also assumed for simplicity
that there is in average N fluxes per particle. If the number N of fluxes is
even, then the system can be identified as composite fermions. If N is odd,
then we obtain composite bosons. Quantization is described as gradation by
certain abelian group G. Statistics is determined by a commutation factor on
the grading group G. It is schown that for N = 2 there is a state for which the
magnetic field is completely compensatad by the system of quasiparticles and
for N = 3 the Landau levells are fractionally filled like in the fractional
quantum Hall effect.
