Solvability of commutative right-nilalgebras satisfying (b(aa))a=b((aa)a)*

Authors

  • Iván Correa Universidad Metropolitana de Ciencias de la Educación.
  • Roy Hentzel Iowa State University
  • Alicia Labra Universidad de Chile.

DOI:

https://doi.org/10.4067/10.4067/S0716-09172010000100002

Keywords:

Polynomial identity, Nilpotency, Solvability, Right-nil algebra, identidad polinomial, solubilidad, nilpotencia, álgebra nil-derecha.

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.

Author Biographies

Iván Correa, Universidad Metropolitana de Ciencias de la Educación.

Departamento de Matemática.

Roy Hentzel, Iowa State University

Department of Mathematics.

Alicia Labra, Universidad de Chile.

Facultad de Ciencias.
Departamento de Matemáticas,

References

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

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).

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

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).

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

Published

2011-01-06

How to Cite

[1]
I. Correa, R. Hentzel, and A. Labra, “Solvability of commutative right-nilalgebras satisfying (b(aa))a=b((aa)a)*”, Proyecciones (Antofagasta, On line), vol. 29, no. 1, pp. 9-15, Jan. 2011.

Issue

Section

Artículos