We show that the solution space of the noncommutative KP hierarchy is the
same as that of the commutative KP hierarchy owing to the Birkhoff
decomposition of groups over the noncommutative algebra. The noncommutative
Toda hierarchy is introduced. We derive the bilinear identities for the
Baker--Akhiezer functions and calculate the N-soliton solutions of the
noncommutative Toda hierarchy.Comment: 7 pages, no figures, AMS-LaTeX, minor corrections, final version to
appear in Journal of Physics