On Certain Identity Related to Herstein Theorem on Jordan Derivations |
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| Authors: | Maja Fošner Benjamin Marcen Nejc Širovnik |
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| Institution: | 1.Faculty of Logistics,University of Maribor,Celje,Slovenia;2.Department of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics,University of Maribor,Maribor,Slovenia |
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| Abstract: | Let R be a 6-torsion-free prime ring and let \({D : R \rightarrow R}\) be an additive mapping satisfying the relation 2D(x 4) = D(x 3)x + x 3 D(x) + D(x)x 3 + xD(x 3) for all \({x \in R}\) . The purpose of this paper is to show that D is a derivation. This result is related to a classical result of Herstein, which states that any Jordan derivation on a 2-torsion-free prime ring is a derivation. |
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