The present study is about commutative Jordan nilalgebras of nilindex 4 generated by at most three elements over a field K of characteristic ≠ 2, 3. We first look at the case where such algebras are generated  by two elements and satisfy Engel’s third or fourth condition, then we consider the case where they are generated by three elements and satisfy Engel’s third condition. We prove that these algebras are nilpotent, and hence solvable, while giving a bound of the index of solvability and nilpotency.

commutative nilalgebras, Jordan algebras, Engel's algebras.

Received: October 7, 2022; Revised: December 5, 2022; Accepted: December 15, 2022; Published: December 20, 2022

How to cite this article: Joseph Bayara and Baba Philippe Dakouo, Commutative Jordan nilalgebras of nilindex 4 generated by at most three elements, JP Journal of Algebra, Number Theory and Applications 60(1) (2023), 1-17. http://dx.doi.org/10.17654/0972555523001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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