We study the Hubbard model on a hypercubic lattice with regard to the
possibility of itinerant ferromagnetism. Dynamical mean-field theory i
s used to map the lattice model on an effective local problem, which i
s treated with the help of the noncrossing approximation. By investiga
ting spin-dependent one-particle Green's functions and the magnetic su
sceptibility, a region with nonvanishing ferromagnetic polarization is
found in the limit U-->infinity. The delta-T phase diagram as well as
thermodynamic quantities are discussed. The dependence of the Curie t
emperature on the Coulomb interaction and the competition between ferr
omagnetism and antiferromagnetism are studied in the large-Ci Limit of
the Hubbard model.