  The generalized *-products, or the $*_N$-products, appear both in the
one-loop effective action of noncommutative Yang-Mills theories and in the
coupling of a closed string to N open strings on a disk when the D-brane
world-volume is noncommutative. Factorization of the string amplitudes provides
a uniform understanding of the $*_N$-products and a hint to obtain a simple,
explicit formula (in the momentum space) for arbitrary N in the non-Abelian
case. Possible extension to a more general ${}_M *_{N}$-product in the M-loop
context is discussed.
