Results on Generalized Skew Bi-Semiderivation in Prime Rings

Let \(\mathcal {R}\) be a prime ring of \(char\ne 2, 3\) , \(\mathcal {D}\) a symmetric skew bi-semiderivation of \(\mathcal {R}\) associated with automorphism \(\alpha \) and \(\varDelta \) be a symmetric generalized skew bi-semiderivation associated with \(\alpha , f, \mathcal {D}\) , where f is surjective map and \(\alpha \) is an automorphism. If \(x\varDelta (x,x)=0\) for all \(x\in \mathcal {R}\) , then \(\varDelta =0\) .