  By using a set of scaling limits, the authors in \cite{ADFL,SS} proposed a
framework of deriving the Hall-MHD equations from the two-fluids Euler-Maxwell
equations for electrons and ions. In this paper, we derive the Hall-MHD
equations from the Navier-Stokes-Maxwell equations with generalized Ohm's law
in a mathematically rigorous way via the spectral analysis and energy methods.
