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.
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