Beitr Algebra Geom DOI 10.1007/s13366-015-0246-6 ORIGINAL PAPER On Lie higher derivable mappings on prime rings Mohammad Ashraf 1 · Nazia Parveen 1 Received: 10 November 2014 / Accepted: 25 March 2015 © The Managing Editors 2015 Abstract Let R be a prime ring containing a nontrivial idempotent. We say that a fam- ily of maps D ={d n } n∈N is a Lie higher derivable map (without assumption of addi- tivity) if d 0 = id R (the identity map on R) and d n ([a, b]) = ∑ p+q =n [d p (a), d q (b)] for all a, b ∈ R and for all n ∈ N. In the present paper it is shown that if D is a Lie higher derivable then there exists an element z a,b (depending on a and b) in its center Z ( R) such that d n (a + b) = d n (a) + d n (b) + z a,b . Keywords Prime ring · Derivations · Higher derivation · Lie derivable maps Mathematics Subject Classification 16W25 · 16N60 · 16U80 1 Introduction Let R be a ring. An additive mapping d : R → R is said to be a derivation (resp. Lie derivation) if d (ab) = d (a)b + ad (b) (resp. d ([a, b]) =[d (a), b]+[a, d (b)]), holds true for all a, b ∈ R, where [a, b]= ab - ba is the usual Lie product of a and b. It is not difficult to observe that any derivation is a Lie derivation. However, the converse statement is in general not true, which can be seen by the example: let d : R → R be a derivation and g : R → Z ( R) be an additive mapping with g([ R, R]) = 0. Then d + g is a Lie derivation, which is not a derivation. Also an additive map d : R → R is said to be Jordan derivation if d (ab + ba) = d (a)b + ad (b) + d (b)a + bd (a), holds for all a, b ∈ R. B Mohammad Ashraf mashraf80@hotmail.com Nazia Parveen naziamath@gmail.com 1 Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India 123