Proyecciones Journal of Mathematics
Vol. 29, N° 1, pp. 9-15, May 2010.
Universidad Católica del Norte
Antofagasta - Chile


SOLVABILITY OF COMMUTATIVE RIGHT-NILALGEBRAS SATISFYING (b(aa))a = b((aa)a)*


Iván Correa
Irvin Roy Hentzel
Alicia Labra

Universidad De Chile, Chile


Correspondencia a:

Abstract

We study commutative right-nilalgebras of right-nilindex four satisfying the identity (b(aa))a = b((aa)a). Our main result is that these algebras are solvable and not necessarily nilpotent. Our results require characteristic ≠ 2, 3, 5.

2000 Mathematics Subject Classification : 17 A30.

Keywords : Polynomial identity: Nilpotency; Solvability; Rightnilalgebra.

References

[1] I. R. Hentzel, A. Labra, Generalized Jordan algebras, Linear Alg. and its Applications 422, pp. 326-330, (2007).        [ Links ]

[2] D. P. Jacobs, D. Lee, S. V. Muddana, A. J. Offut, K. Prabhu, T. Whiteley, Albert's User Guide. Department of Computers Science, Clemson University, (1993).        [ Links ]

[3] R. D. Schafer, An introduction to Nonassociative Algebras, Academic Press, New York - San Francisco - London, (1966).        [ Links ]

[4] K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov, A. I. Shirshov, Rings that are nearly associative, Academic Press, New York - San Diego - San Francisco, (1982).        [ Links ]

[5] E. I. Zelmanov, V. G. Skosyrskii, Special Jordan nil algebras of bounded index, Algebra and Logik 22 (6), pp. 626-635, (1983).        [ Links ]

Received : July 2009. Accepted : December 2010

Iván Correa
Departamento de Matemática
Universidad Metropolitana de Ciencias de la Educación
J. P. Alessandri 774 - Santiago - Chile
e-mail : ivan.correa@umce.cl


Roy Hentzel
Department of Mathematics
Iowa State University
Ames - Iowa 50011-2064
e-mail : hentzel@iastate.edu


Alicia Labra
Departamento de Matemáticas
Facultad de Ciencias
Universidad de Chile, Casilla 653, Santiago - Chile
e-mail : alimat@uchile.cl