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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.23 no.2 Antofagasta Aug. 2004

http://dx.doi.org/10.4067/S0716-09172004000200005 

 

Proyecciones
Vol. 23, No 2, pp. 123-129, August 2004.
Universidad Católica del Norte
Antofagasta - Chile

SOLVABILITY OF COMMUTATIVE POWER-ASSOCIATIVE NILALGEBRAS OF NILINDEX 4 AND DIMENSION

 

LUISA ELGUETA and AVELINO SUAZO

Universidad de La Serena, Chile

Received : October 2003. Accepted : May 2004

correspondencia a:


Abstract

Let A be a commutative power-associative nilalgebra: In this paper we prove that when A (of characteristic ≠ 2) is of dimension < 8 and x4 = 0 for all x A; then ((A2)2)2 = 0: That is, A is solvable. We conclude that if A is of dimension < 7 over a field of characteristic2, 3 and 5; then A is solvable.


3. REFERENCES

[1] Correa, I.; Suazo, A. On a class of commutative power-associative nilalgebras. Journal of Algebra, 215, pp. 412-417, (1999).

[2] Correa, I.; Hentzel I. R.; Peresi, L. A. On the solvability of the commutative power-associative nilalgebras of dimension 6. Linear Alg. Appl., 369, pp. 185-192, (2003).

[3] Elgueta, L.; Suazo, A. Jordan nilalgebras of nilindex n and dimension n +1. Communications in Algebra, 30, pp. 5547-5561, (2002).

[4] Elgueta, L.; Gutierrez Fernandez, J. C.; Suazo, A. Nilpotence of a class of commutative power-associative nilalgebras. Submitted.

[5] Gerstenhaber, M.; Myung, H.C. On commutative power-associative nilalgebras of low dimension. Proc. Amer. Math. Soc., 48, pp. 29-32, (1975).

[6] Gutierrez Fernandez J.C. On commutative power-associative nilalgebras. Communications in Algebra, 32(6), pp. 2243-2250, (2004).

[7] Schafer, R.D. An Introduction to Nonassociative Algebras; Academic Press: New York/London, (1966).

[8] Suttles, D.A. Counterexample to a conjeture ofAlbert. Notices Amer. Math. Soc. , 19, A-566, (1972).

[9] Zhevlakov, K.A.; Slin'ko, A.M.; Shestakov, I.P.; Shirshov, A.I. Rings That Are Nearly Associative; Academic Press: New York/London, (1992).

Luisa Elgueta
Departamento de Matemáticas
Universidad de La Serena
Cisternas 1200
La Serena
Chile
e-mail : lelgueta@userena.cl

and

Avelino Suazo
Departamento de Matemáticas
Universidad de La Serena
Cisternas 1200
La Serena
Chile
e-mail : asuazo@userena.cl

 

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