Multiplicative generalized Lie n-derivations of unital rings with idempotents

Let u be a unital ring with a nontrivial idempotent. In this paper, it is shown that under certain conditions every multiplicative generalized Lie n-derivation Delta : u -> u is of the form Delta(u) = zu + delta(u), where z is an element of Z(u) and delta : u -> u is a multiplicative Lie n-derivation. The main result is then applied to some classical examples of unital rings with nontrivial idempotents such as triangular rings, matrix rings, nest algebras, and algebras of bounded linear operators.