  By considering N_e-electrons and N_h-holes together in uniform external
magnetic and electric fields, we end up with a total Hall conductivity
\sigma_{H}^{tot}, which is depending to the difference between N_e and N_h and
becomes null when N_e=N_h. Dealing with the same system but requiring that the
coordinates of plane are noncommuting, we obtain a new Hall conductivity
\sigma_{H}^{(tot,nc)}. In the limit N_e=N_h, we find that \sigma_{H}^{(tot,nc)}
is only noncommutativity parameters \theta_i-dependent, which means that
theoretically it is possible to have Hall effect without B. Moreover, at the
critical points \theta_e=l^2 and \theta_h=-l^2, we find that
\sigma_{H}^{(tot,nc)} becomes two times the usual Hall conductivity for an
noninteracting mixing system.
