Two Iterates of Symmetric Generalized Skew 3-Derivation

Abstract

Our goal in this study is to validate the following finding: Assume that a prime ring R having , D is a symmetric skew 3-derivation on R with automorphisms α. If ∇₁, ∇₂ : R³ → R are symmetric generalized skew 3-derivations with α and associated skew 3-derivations D₁, D₂ respectively such that for every , then either ∇₁ = 0 or ∇₂ = 0 on R, where ∂₁ and ∂₂ stands for the traces of ∇₁ and ∇₂ respectively.