ADDITIVITY OF JORDAN n-TUPLE DERIVABLE MAPS ON ALTERNATIVE RINGS

Abstract

Let R be an alternative ring. We study the additivity of maps δ : R → R satisfying the following condition δ(an ◦ (···(a2 ◦ a1)···)) = n k=1 an◦(···(δ(ak)◦(···(a2◦a1)···))···) for all a1,···,an ∈ R, wherea ◦b = ab + ba is the Jordan product of a and b in R. We prove that if R contains a non-trivial idempotent satisfying some conditions, then δ is additive.