Arabian Journal of Mathematics

, Volume 6, Issue 2, pp 75–78 | Cite as

What can be expected from a cubic derivation on finite dimensional algebras?

  • Amin Hosseini
Open Access


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.

Mathematics Subject Classification

47B47 47B48 


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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsKashmar Higher Education InstituteKashmarIran

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