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The Adler-Bell-Jackiw (ABJ) anomaly of a 3+1 dimensional QED is calculated inthe presence of a strong magnetic field. It is shown that in the regime withthe lowest Landau level (LLL) dominance a dimensional reduction from D=4 to D=2dimensions occurs in the longitudinal sector of the low energy effective fieldtheory. In the chiral limit, the resulting anomaly is therefore comparable withthe axial anomaly of a two dimensional massless Schwinger model. It is furthershown that the U(1) axial anomaly of QED in a strong magnetic field is closelyrelated to the ``nonplanar'' axial anomaly of a conventional noncommutativeQED.Comment: 18 pp, no figure. v2: The version accepted to be publidhed in PR

Axial anomaly of QED in a strong magnetic field and noncommutative anomaly