  We discuss the role that interactions play in the non-commutative structure
that arises when the relative coordinates of two interacting particles are
projected onto the lowest Landau level. It is shown that the interactions in
general renormalize the non-commutative parameter away from the non-interacting
value $\frac{1}{B}$. The effective non-commutative parameter is in general also
angular momentum dependent. An heuristic argument, based on the non-commutative
coordinates, is given to find the filling fractions at incompressibilty, which
are in general renormalized by the interactions, and the results are consistent
with known results in the case of singular magnetic fields.
