Ukrainian Mathematical Journal

, Volume 66, Issue 10, pp 1609–1614

# Remarks on Certain Identities with Derivations on Semiprime Rings

• A. Fošner
• N. Baydar
• R. Strašek
Article

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 1 2 (x) + D 2(x)) n  ∘ α(x) n  = 0 holds for all xR, 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 xR, where F(x) = (D 1 2 (x) + D 2(x)) ∘ α(x), x ∈ R, and β is any automorphism or antiautomorphism on R.

## Keywords

Positive Integer Additive Mapping Prime Ring Associative Ring Semiprime Ring
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## Authors and Affiliations

• A. Fošner
• 1
• N. Baydar
• 2
• R. Strašek
• 1
1. 1.University of PrimorskaKoperSlovenia
2. 2.Ege UniversityIzmirTurkey