Manuel Arenas, Iván Correa, I. Hentzel, Alicia Labra
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引用次数: 0
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.
期刊介绍:
The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.