Abstract
In this paper we prove the following result. Let m ≥ 1, n ≥ 1 be fixed integers and let R be a prime ring with m + n + 1 ≤ char(R) or char(R) = 0. Suppose there exists an additive nonzero mapping D : R → R satisfying the relation 2D(x n+m+1) = (m + n + 1)(x m D(x)x n + x n D(x)x m) for all \({x\in R}\). In this case R is commutative and D is a derivation.
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Communicated by John S. Wilson.
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Fošner, M., Peršin, N. On a functional equation related to derivations in prime rings. Monatsh Math 167, 189–203 (2012). https://doi.org/10.1007/s00605-011-0319-z
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DOI: https://doi.org/10.1007/s00605-011-0319-z
Keywords
- Prime ring
- Semiprime ring
- Derivation
- Jordan derivation
- Left derivation
- Left Jordan derivation
- Commuting mapping
- Centralizing mapping
- Functional identity