Certain Additive Maps on (m+n+1)-Power Closed Lie Ideals

Abstract

Let R be a prime ring and m, n be fixed non-negative integers such that m+n ≠ 0. Suppose L is an (m+n+1)-power closed Lie ideal, and this means um+n+1∈ L for all u ∈ L. If char R=0 or a prime p > 2(m+n), we characterize the additive maps d: L → R satisfying d(um+n+1)=(m+n+1)umd(u)un (resp., d(um+n+1)=umd(u)un) for all u ∈ L.