# On train algebras of degree 2 and exponent 4

## Main Article Content

## Abstract

In this paper, we deal with a class of nonassociative algebras called train algebras of degree *2* and exponent *4*; Thus we give some results on algebras verifying a train identity of degree *2* and exponent *4*. The structure of this class of algebras is studied through Peirce decomposition relative to a non zero idempotent. We give the necessary and sufficient conditions for an algebra verifying a train identity of degree *2* and exponent *4* to be Bernstein or train algebra of rank less than or equal to *3*. Finally, we give some necessary conditions that must be verified by a train algebra of degree *2* and exponent *4*, mainly in dimension four.

## Article Details

How to Cite

*Gulf Journal of Mathematics*,

*13*(1), 41-53. Retrieved from https://gjom.org/index.php/gjom/article/view/926

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