Abstract
The generalized * products, or the *{sub 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 *{sub 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 {sub M}*{sub N}-product in the M-loop context is discussed.
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