Let n be a fixed positive integer, let R be a (2n)! -torsion-free semiprime ring, let \( \alpha \) be an automorphism or an anti-automorphism of R, and let D 1 , D 2 : R → R be derivations. We prove the following result: If (D 21 (x) + D 2(x))n ∘ α(x)n = 0 holds for all x ∈ R, then D 1 = D 2 = 0. The same is true if R is a 2-torsion free semiprime ring and F(x) ° β(x) = 0 for all x ∈ R, where F(x) = (D 21 (x) + D 2(x)) ∘ α(x), x ∈ R, and β is any automorphism or antiautomorphism on R.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 10, pp. 1436–1440, October, 2014.
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Fošner, A., Baydar, N. & Strašek, R. Remarks on Certain Identities with Derivations on Semiprime Rings. Ukr Math J 66, 1609–1614 (2015). https://doi.org/10.1007/s11253-015-1037-9
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DOI: https://doi.org/10.1007/s11253-015-1037-9