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We study a system of electrons moving on a noncommutative plane in thepresence of an external magnetic field which is perpendicular to this plane.For generality we assume that the coordinates and the momenta are bothnoncommutative. We make a transformation from the noncommutative coordinates toa set of commuting coordinates and then we write the Hamiltonian for thissystem. The energy spectrum and the expectation value of the current can thenbe calculated and the Hall conductivity can be extracted. We use the samemethod to calculate the phase shift for the Aharonov-Bohm effect. Precessionmeasurements could allow strong upper limits to be imposed on thenoncommutativity coordinate and momentum parameters $\Theta$ and $\Xi$.Comment: 9 pages, RevTeX4, references added, small changes in the tex

Noncommutative quantum Hall effect and Aharonov–Bohm effect