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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
Article
  • 149 Downloads

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.

Mathematics Subject Classification

47B47 47B48 

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), 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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