Affiliation:
1. Universidad Tecnologica Metropolitana
2. Universidad Metropolitana Ciencias de la Educacion
3. Iowa State University
4. Universidad de Chile
Abstract
We study commutative algebras satisfying the identity
$ ((wx)y)z+((wy)z)x+((wz)x)y-((wy)x)z- ((wx)z)y-((wz)y)x = 0. $ We assume
characteristic of the field $\neq 2,3.$ We prove that given any $\lambda \in F,$ there exists a commutative algebra with idempotent $e,$ which satisfies the identity, and has $\lambda $ as an eigen value of the multiplication operator $L_e$. For algebras with idempotent, the containment relations for the product of the eigen spaces are not as precise as they are for Jordan or power-associative algebras. A great part of this paper is calculating these containment relations.
Publisher
The International Electronic Journal of Algebra
Reference9 articles.
1. A. A. Albert, Power-associative rings, Trans. Amer. Math. Soc., 64 (1948), 552-593.
2. L. Carini, I. R. Hentzel and G. M. Piacentini Cattaneo, Degree four identities not implied by commutativity, Comm. Algebra, 16(2) (1988), 339-356.
3. I. Correa and I. R. Hentzel, Commutative non associative nil algebras satisfying an identity of degree four, Preprint (2023).
4. M. Gerstenhaber, On nilalgebras and linear varieties of nilpotent matrices II, Duke Math. J., 27 (1960), 21-31.
5. D. P. Jacobs, S. V. Muddana and A. J. Offutt, A computer algebra system for nonassociative identities, Hadronic mechanics and nonpotential interactions, Nova Science Publishers, Inc., Commack, NY, Part 1 (Cedar Falls, IA, 1990) (1992), 185-195.