Keywords and phrases: commutative nilalgebras, Jordan algebras, Engel's algebras.
Received: October 7, 2022; Revised: December 5, 2022; Accepted: December 15, 2022; Published: December 20, 2022
How to cite this article: Joseph Bayara and Baba Philippe Dakouo, Commutative Jordan nilalgebras of nilindex 4 generated by at most three elements, JP Journal of Algebra, Number Theory and Applications 60(1) (2023), 1-17. http://dx.doi.org/10.17654/0972555523001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] I. Correa and I. R. Hentzel, Commutative finitely generated algebras satisfying are solvable, Rocky Mountain J. Math. 39(3) (2009), 757-764. [2] I. Correa, I. R. Hentzel and A. Labra, Nilpotency of commutative finitely generated algebras satisfying J. Algebra 330 (2011), 48-59. [3] I. Correa, I. R. Hentzel and L. A. Peresi, On the solvability of the commutative power associative nilalgebras of dimension 6, Linear Algebra Appl. 369 (2003), 185-192. [4] L. Elgueta and A. Suazo, Jordan nilalgebras of dimension 6, Proyecciones 21(3) (2002), 277-289. [5] L. Elgueta and A. Suazo, Jordan nilalgebras of nilindex n and dimension Comm. Algebra 30(11) (2002), 5547-5561. [6] L. Elgueta, A. Suazo and J. C. Fernandez, Nilpotence of a class of commutative power-associative nilalgebras, J. Algebra 291 (2005), 492-504. [7] J. C. Fernandez and I. Claudia, On Jordan nilalgebras of index 3, Comm. Algebra 44(10) (2016), 4277-4293. [8] M. Gerstenhaber, On nilalgebras and linear varieties of nilpotent matrices II, Duke Math. J. 27 (1960), 21-31. [9] R. D. Schafer, An Introduction to Nonassociative Algebras, Academic Press, New York, London, 1966. [10] D. A. Suttles, A counterexample to a conjecture of Albert, Not. Am. Math. Soc. 19 (1972), A-566. [11] E. I. Zelmanov, Jordan nil algebra of bounded index, Dokl. Akad. Nauk SSSR 249(1) (1979), 30-33. [12] K. A. Zhevlakov, A. M. Slin’Ko, I. P. Shestakov and A. I. Shirshov, Rings that are Nearly Associative, Academic Press, New York, 1982.
|