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STRUCTURE OF BARIC ALGEBRAS SATISFYING A POLYNOMIAL IDENTITY OF DEGREE SIX
Keywords:
Peirce decomposition, Bernstein algebra, Jordan algebra, power associative algebra, polynomial identity, idempotent, type of an algebraAbstract
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.
Received: February 7, 2023
Accepted: March 23, 2023
References
M. T. Alcalde, C. Burgueño, A. Labra and A. Micali, Sur les algèbres de Bernstein (on Bernstein algebras), Proc. Lond. Math. Soc. (3) 58(1) (1989), 51-68.
J. Bayara, A. Conseibo, M. Ouattara and A. Micali, Train algebras of degree 2 and exponent 3, Discrete and Continuous Dynamical Systems Series 4(6) (2011), 1971-1986.
J. Bayara, A. Conseibo, M. Ouattara and F. Zitan, Power-associative algebras that are train algebras, J. Algebra 324 (2010), 1159-1176.
A. A. Albert, A theory of power-associative commutative algebras, Trans. Amer. Math. Soc. 69 (1950), 503-527.
S. Bernstein, Solution of a mathematical problem connected with the theory of heredity, Ann. Math. Stat. 13 (1942), 53-61.
D. Schafer Richard, Introduction to Nonassociative Algebras, Academic Press, New York, 1966.
J. S. Lopez and E. S. M. Rodriguez, On train algebras of rank 4, Comm. Algebra 24(14) (1996), 4439-4445.
J. G. F. Carlos, Principal and plenary train algebras, Comm. Algebra 28(2) (2000), 653-667.
P. Holgate, Genetic algebras satisfying Bernstein’s stationarity principle, J. London Math. Soc. (2) 9 (1974/75), 612-623.
S. Walcher, Bernstein algebras which are Jordan algebras, Arch. Math. 50(3) (1988), 218-222.
A. Wörz-Busekros, Algebras in genetics, Lecture Notes in Biomathematics, 36, Springer-Verlag, Berlin-New York, 1980.
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