Abstract
In this paper, we prove that every rank one cubic derivation on a unital integral domain is identically zero. From this conclusion, under certain conditions, we achieve that the image of a cubic derivation on a commutative algebra is contained in the Jacobson radical of algebra. As the main result of the current study, we prove that every cubic derivation on a finite dimensional algebra, under some circumstances, is identically zero.
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Hosseini, A. What can be expected from a cubic derivation on finite dimensional algebras?. Arab. J. Math. 6, 75–78 (2017). https://doi.org/10.1007/s40065-017-0168-2
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DOI: https://doi.org/10.1007/s40065-017-0168-2