  The current through ferromagnetic single-electron transistors (SET's) is
considered. Using path integrals the linear response conductance is formulated
as a function of the tunnel conductance vs. quantum conductance and the
temperature vs. Coulomb charging energy. The magneto-resistance of
ferromagnet-normal metal-ferromagnet (F-N-F) SET's is almost independent of the
Coulomb charging energy and is only reduced when the transport dwell time is
longer than the spin-flip relaxation time. In all-ferromagnetic (F-F-F) SET's
with negligible spin-flip relaxation time the magneto-resistance is calculated
analytically at high temperatures and numerically at low temperatures. The
F-F-F magneto-resistance is enhanced by higher order tunneling processes at low
temperatures in the 'off' state when the induced charges vanishes. In contrast,
in the 'on' state near resonance the magneto-resistance ratio is a
non-monotonic function of the inverse temperature.
