Abstract
In this paper we prove the following result: Let R be a prime ring with \({\text {char}}(R)\ne 2,3,5\) and let \( T :R \rightarrow R\) be an additive mapping satisfying the relation \( 3T(x^{4})=T(x)x^{3}+xT(x^2)x+x^{3}T(x)\) for all \(x\in R\). In this case T is of the form \(T(x)=\lambda x\) for all \(x\in R\) and some fixed element \(\lambda \in C\), where C is the extended centroid of R.
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Fošner, M., Marcen, B. & Vukman, J. On a functional equation characterizing two-sided centralizers in prime rings. Period Math Hung 86, 538–551 (2023). https://doi.org/10.1007/s10998-022-00489-z
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DOI: https://doi.org/10.1007/s10998-022-00489-z
Keywords
- Ring
- Prime ring
- Semiprime ring
- Derivation
- Jordan derivation
- Jordan triple derivation
- Left (right) centralizer
- Left (right) Jordan centralizer
- Two-sided centralizer
- Functional equation
- Functional identity