  The decomposition of the non-commutative Landau (NCL) system into two
uncoupled one-dimensional chiral components, advocated by Alvarez, Gomis,
Kamimura and Plyushchay [1], is generalized to nonvanishing electric fields.
This allows us to discuss the main properties of the NCL problem including its
exotic Newton-Hooke symmetry and its relation to the Hall effect. The "phase
transition" when the magnetic field crosses a critical value determined by the
non-commutative parameter is studied in detail.
