It is known that commutative power-associative nilalgebras of nilindex 4 are not necessarily nilpotent. This was proved by Suttles’ counterexample to a conjecture of Albert. This article is about commutative non-associative algebras of characteristic  which satisfy the identity  These algebras are nilpotent if they are finite dimensional. For dimension 3 or 4, commutative nilalgebras of index 4 are such algebras. For dimension  power-associativity implies that they are Jordan algebras. For dimension 6, if they are power-associative but not Jordan algebras, then they are nilpotent of index 5 and solvable of index 3.

commutative, Jordan, power-associative, nilalgebra, nilpotent, solvable

Received: August 3, 2024; Accepted: November 23, 2024; Published: December 5, 2024

How to cite this article: Joseph BAYARA and Poussyan Patrice OUEDRAOGO, Commutative algebras satisfying identity x³y = 0, JP Journal of Algebra, Number Theory and Applications 64(1) (2025), 27-46. https://doi.org/10.17654/0972555525003

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

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