On conmutative left-nilalgebras of index 4
DOI:
https://doi.org/10.4067/S0716-09172008000100007Keywords:
Solvable, commutative, nil-algebra, soluble, conmutativa.Abstract
We first present a solution to a conjecture of (Correa, Hentzel, Labra, 2002) in the positive. We show that if A is a commutative nonassociative algebra over a field of characteristic 6= 2, 3, satisfying the identity x(x(xx)) = 0, then Lat1 Lat2 · · · Lats 
0 if t1 + t2 + · · · + ts 10, where a 
A.
References
[1] Albert, A. A.. Power-associative rings. Trans. Amer. Math. Soc. 64 : pp. 552-593, (1948).
[2] Correa, I., Hentzel I.R., Labra, A. (2002). On the nilpotence of the multiplication operator in commutative right nil algebras. Comm. in Algebra 30, pp. 3473-3488, (2002).
[3] Elduque, A., Labra, A.. On the Classification of commutative right-nilalgebras of dimension at most four. Comm. in Algebra 35 : pp. 577-588, (2007).
[4] Elgueta, L., Suazo, A.. Solvability of commutative power-associative nilalgebras of nilindex 4 and dimension ? 8. Proyecciones 23 : pp. 123-129, (2004).
[5] Elgueta, L., Fernandez, J. C. G., Suazo, A.. Nilpotence of a class of commutative power-associative nilalgebras. Journal of Algebra 291 : pp. 492-504, (2005).
[6] Fernandez, J. C. G.. On commutative power-associative nilalgebras. Comm. in Algebra 32 : pp. 2243-2250, (2004).
[7] Fernandez, J. C. G., Suazo, A.. Commutative power-associative nilalgebras of nilindex 5. Result. Math. 47 : pp. 296-304, (2005).
[8] Gerstenhaber, M.. On nilalgebras and linear varieties of nilpotent matrices II. Duke Math. J. 27 : pp. 21-31, (1960).
[9] Osborn, J. M.. Varieties of algebras. Adv. in Math. 8 : pp. 163-396, (1972).
[10] Zhevlakov, K. A., Slinko, A. M., Shestakov, I. P., Shirshov, A. I.. Rings that are nearly associative. Academic Press, New York, (1982).
[2] Correa, I., Hentzel I.R., Labra, A. (2002). On the nilpotence of the multiplication operator in commutative right nil algebras. Comm. in Algebra 30, pp. 3473-3488, (2002).
[3] Elduque, A., Labra, A.. On the Classification of commutative right-nilalgebras of dimension at most four. Comm. in Algebra 35 : pp. 577-588, (2007).
[4] Elgueta, L., Suazo, A.. Solvability of commutative power-associative nilalgebras of nilindex 4 and dimension ? 8. Proyecciones 23 : pp. 123-129, (2004).
[5] Elgueta, L., Fernandez, J. C. G., Suazo, A.. Nilpotence of a class of commutative power-associative nilalgebras. Journal of Algebra 291 : pp. 492-504, (2005).
[6] Fernandez, J. C. G.. On commutative power-associative nilalgebras. Comm. in Algebra 32 : pp. 2243-2250, (2004).
[7] Fernandez, J. C. G., Suazo, A.. Commutative power-associative nilalgebras of nilindex 5. Result. Math. 47 : pp. 296-304, (2005).
[8] Gerstenhaber, M.. On nilalgebras and linear varieties of nilpotent matrices II. Duke Math. J. 27 : pp. 21-31, (1960).
[9] Osborn, J. M.. Varieties of algebras. Adv. in Math. 8 : pp. 163-396, (1972).
[10] Zhevlakov, K. A., Slinko, A. M., Shestakov, I. P., Shirshov, A. I.. Rings that are nearly associative. Academic Press, New York, (1982).
Published
2017-05-02
How to Cite
[1]
J. C. Gutierrez Fernandez, “On conmutative left-nilalgebras of index 4”, Proyecciones (Antofagasta, On line), vol. 27, no. 1, pp. 103-111, May 2017.
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