Commutative Finitely Generated Algebras Satisfying ((yx)x)x = 0 are Solvable
We study commutative, nonassociative algebras satisfying the identity
(1) ((yx)x)x = 0
We show that finitely generated algebras over a field K of characteristic ≠ 2 satisfying (1) are solvable. For x in an algebra A, define the multiplicatin operator Rx by yRx = yx, for all y ∈ A. Our identify is then that Rx3 = 0.
This article is published as Correa, Ivan, and Irvin Roy Hentzel. "Commutative Finitely Generated Algebras Satisfying ((yx) x) x= 0 are Solvable." Rocky Mountain Journal of Mathematics 39, no. 3 (2009): 757-764. DOI: 10.1216/RMJ-2009-39-3-757. Posted with permission.