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ON A CLASS OF ALGEBRAS SATISFYING AN IDENTITY OF DEGREE FIVE
Keywords:
generalized almost Jordan algebra, identity of degree five, Peirce decomposition, idempotent, derivation, representation.DOI:
https://doi.org/10.17654/0972555523023Abstract
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.
Received: May 6, 2023
Revised: May 30, 2023
Accepted: July 4, 2023
References
A. A. Albert, Structure theory for Jordan algebras, Ann. of Math. 48(3) (1947), 546-567.
M. Arenas and A. Labra, On nilpotency of generalized almost-Jordan right-nilalgebras, Algebra Colloquium 15 (2008), 69-82.
L. Carini, I. R. Hentzel and J. M. Piaccentini-Cattaneo, Degree four identities not implies by commutativity, Comm. in Algebra 16(2) (1988), 339-357.
S. Eilenberg, Extensions of general algebras, Ann. Soc. Polon. Math. 21 (1948), 125-134.
M. Flores and A. Labra, Representations of generalized almost-Jordan algebras, Comm. in Algebra 43(8) (2015), 3373-3381.
H. Guzzo Jr. and A. Labra, An equivalence in generalized almost-Jordan algebras, Proyecciones 35(4) (2016), 505-519.
I. R. Hentzel and L. A. Peresi, Almost Jordan rings, Proc. Amer. Math. Soc. 104(2) (1988), 343-348.
J. M. Osborn, Commutative algebras satisfying an identity of degree four, Proc. Amer. Math. Soc. 16 (1965), 1114-1120.
R. D. Schafer, Introduction on Nonassociative Algebras, Academic Press, New York, 1966.
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