  The flux line lattice melting transition in two-dimensional pure and
disordered superconductors is studied by a Monte Carlo simulation using the
lowest Landau level approximation and quasi-periodic boundary condition on a
plane. The position of the melting line was determined from the diffraction
pattern of the superconducting order parameter. In the clean case we confirmed
the results from earlier studies which show the existence of a quasi-long range
ordered vortex lattice at low temperatures. Adding frozen disorder to the
system the melting transition line is shifted to slightly lower fields. The
correlations of the order parameter for translational long range order of the
vortex positions seem to decay slightly faster than a power law (in agreement
with the theory of Carpentier and Le Doussal) although a simple power law decay
cannot be excluded. The corresponding positional glass correlation function
decays as a power law establishing the existence of a quasi-long range ordered
positional glass formed by the vortices. The correlation function
characterizing a phase coherent vortex glass decays however exponentially
ruling out the possible existence of a phase coherent vortex glass phase.
