  The relationship between the noncommutativity of operators and the violation
of the Bell inequality is exhibited in the light of the n-particle Bell-type
inequality discovered by Mermin [PRL 65, 1838 (1990)]. It is shown, in
particular, that the maximal amount of violation of Mermin's inequality
predicted by quantum mechanics decreases exponentially by a factor of 2^{-m/2}
whenever any m among the n single-particle commutators happen to vanish.
