  Large masses of absorbing material are inferred to exist in cooling flows in
clusters of galaxies from the excess X-ray absorption in the spectra of some
X-ray clusters. The absorbing material is probably in the form of cold clouds
pressure-confined by the surrounding, hot, X-ray emitting gas. The cold clouds
could remain relatively static until they are destroyed by evaporation or
ablation, or give rise to star formation. If the final fate of the clouds is
stars, the IMF of the stars formed over the whole cooling flow region ($r \sim
100$ kpc) should be biased to low masses, to avoid a very luminous, blue halo
for the central galaxy of the cooling flow. However, there is evidence for
bright star formation in the innermost (r < 10 kpc) regions of some cooling
flows, and, therefore, the biasing of the IMF towards low masses should not
occur or be less important at smaller radii. The consideration of magnetic
fields may shed light on these two points. If magnetic fields are present, the
magnetic critical mass should be considered, besides the Jeans mass, in
establishing a natural mass scale for star formation. When this new mass scale
is taken into account, we obtain the right variation of the biasing of the IMF
with the radius in addition to inhibition of high-mass star formation at large
radii. We also demonstrate that magnetic reconnection is a efficient than
ambipolar diffusion in removing magnetic fields in cold clouds.
