  An effective U(1) gauge invariant theory is constructed for a non-commutative
Schrodinger field coupled to a background U(1)_{\star} gauge field in
2+1-dimensions using first order Seiberg-Witten map. We show that this
effective theory can be cast in the form of usual Schrodinger action with
interaction terms of noncommutative origin provided the gauge field is of
``background'' type with constant magnetic field. The Galilean symmetry is
investigated and a violation is found in the boost sector. We also consider the
problem of Hall conductivity in this framework.
