JP Journal of Algebra, Number Theory and Applications
Volume 62, Issue 2, Pages 87 - 107
(November 2023) http://dx.doi.org/10.17654/0972555523023 |
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ON A CLASS OF ALGEBRAS SATISFYING AN IDENTITY OF DEGREE FIVE
Aly GUIRO, Abdoulaye DEMBEGA and André CONSEIBO
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Abstract: In this paper, we study a class of commutative nonassociative algebras satisfying a polynomial identity of degree five. We show that under the assumption of the existence of a nonzero idempotent, any algebra satisfying such an identity admits a Peirce decomposition. Using this decomposition, we study the derivations and representations of algebras of this class.
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Keywords and phrases: generalized almost Jordan algebra, identity of degree five, Peirce decomposition, idempotent, derivation, representation.
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