Proyecciones
Vol. 21, N o 3, pp. 199-224, December 2002.
Universidad Católica del Norte
Antofagasta - Chile

JORDAN NILALGEBRAS OF DIMENSION 6

LUISA ELGUETA ¤
and
AVELINO SUAZO
Universidad de La Serena, Chile

Abstract

It is known the classification of commutative power-associative nilalgebras of dimension £4 (see, [4]). In [2], we give a description of commutative power-associative nilalgebras of dimension 5. In this work we describe Jordan nilalgebras of dimension 6.

AMS Subject Classification : 17 C 10.

5. REFERENCES

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

[2] L. Elgueta and A. Suazo, Jordan nilagebras of nilindex n and dimension n + 1, Communications in Algebra, Vol. 30, 11, pp. 5545-5559, (2002).

[3] L. Elgueta and A. Suazo, The index of nilpotence of Jordan nilalgebras of nilindex n and dimension £n + 2, International Journal of Mathematics, Game Theory and Algebra, to appear (2002).

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

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

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

Received : June, 2002

Luisa Elgueta
Departamento de Matemáticas
Universidad de La Serena
Benavente 980
La Serena
Chile
e-mail : lelgueta@userena.cl

and

Avelino Suazo
Departamento de Matemáticas
Universidad de La Serena
Benavente 980
La Serena
Chile
e-mail : asuazo@userena.cl

¤Research supported by Conicyt-Chile, Proyecto Fondecyt-Líneas Complementarias 8990001.