Large masses of absorbing material are inferred to exist in cooling flows i
n clusters of galaxies from the excess X-ray absorption in the spectra of s
ome 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 c
old clouds could remain relatively static until they are destroyed by evapo
ration or ablation, or give rise to star formation. If the final fate of th
e clouds is stars, the initial mass function (IMF) of the stars formed over
the whole cooling-flow region (r similar to 100 kpc) should be biased to l
ow masses, to avoid a very luminous, blue halo for the central galaxy of th
e cooling flow. However, there is evidence for bright star formation in the
innermost (r less than or similar to 10 kpc) regions of some cooling flows
, and, therefore, the biasing of the IMF towards low masses should not occu
r or should be less important at smaller radii. The consideration of magnet
ic fields may shed light on these two points. If magnetic fields are presen
t, the magnetic critical mass should be considered, besides the Jeans mass,
in establishing a natural mass-scale for star formation. When this new mas
s-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 for
mation at large radii. We also demonstrate that magnetic reconnection is a
more efficient mechanism than ambipolar diffusion to remove magnetic fields
in cold clouds.