Generalized Lie-Type Derivations of Alternative Algebras

In this paper we intend to describe generalized Lie-type derivations using, among other things, a generalization for alternative algebras of the result: "If F : A -> A is a generalized Lie n-derivation associated with a Lie n-derivation D, then a linear map H = F - D satisfies H(p(n)(x(1), x(2),..., x(n))) = p(n)(H(x(1)), x(2),..., x(n)) for all x(1), x(2),..., x(n) is an element of A". Thus, if A is a unital alternative algebra with a nontrivial idempotent e1 satisfying certain conditions, then a generalized Lie-type derivation F : A -> A is of the form F(x) = lambda x+Xi(x) for all x is an element of A, where lambda is an element of Z(A) and Xi : A -> A is a Lie-type derivation.