  The Adler-Bell-Jackiw (ABJ) anomaly of a 3+1 dimensional QED is calculated in
the presence of a strong magnetic field. It is shown that in the regime with
the lowest Landau level (LLL) dominance a dimensional reduction from D=4 to D=2
dimensions occurs in the longitudinal sector of the low energy effective field
theory. In the chiral limit, the resulting anomaly is therefore comparable with
the axial anomaly of a two dimensional massless Schwinger model. It is further
shown that the U(1) axial anomaly of QED in a strong magnetic field is closely
related to the ``nonplanar'' axial anomaly of a conventional noncommutative
QED.
