GENERALIZED LIE DERIVATIONS OF UNITAL ALGEBRAS WITH IDEMPOTENTS

Let A be a unital algebra with a nontrivial idempotent e over a unital commutative ring R. We show that under suitable assumptions every generalized Lie n-derivation F : A -> A is of the form F(x) = lambda x + Delta(x), where lambda is an element of Z(A) and Delta is a Lie n-derivation of A. As an application, we give a description of generalized Lie n -derivations on classical examples of unital algebras with idempotents: triangular algebras, matrix algebras, nest algebras and algebras of all bounded linear operators.