In this paper, we study the structure of a class of algebras satisfying a polynomial identity of degree six. We show, assuming the existence of a non-zero idempotent, that if an algebra satisfies such an identity, it admits a Peirce decomposition related to this idempotent. We studied the algebraic structure and highlighted the connections of the algebras of this class with Bernstein algebras, Jordan algebras and power associative algebras.

Peirce decomposition, Bernstein algebra, Jordan algebra, power associative algebra, polynomial identity, idempotent, type of an algebra.

Received: February 7, 2023; Accepted: March 23, 2023; Published: April 4, 2023

How to cite this article: Daouda KABRE and André CONSEIBO, Structure of baric algebras satisfying a polynomial identity of degree six, JP Journal of Algebra, Number Theory and Applications 61(1) (2023), 37-52. http://dx.doi.org/10.17654/0972555523010

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

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