Lie n-centralizers by local action at the zero products on generalized matrix algebras

Let [Formula: see text] be a generalized matrix algebra over a commutative ring. In this paper, we characterize the linear mapping [Formula: see text] satisfying condition [Formula: see text] as follows: [Formula: see text] [Formula: see text] for all [Formula: see text] with [Formula: see text]. Besides, we apply the results above to some other operator algebras.