On Nilpotency of Generalized Almost-Jordan Right-Nilalgebras

Abstract

We study the variety of algebras A over a field of characteristic ≠ 2, 3, 5 satisfying the identities xy=yx and β {((xx)y)x-((yx)x)x} + γ {((xx)x)y-((yx)x)x}=0, where β, γ are scalars. We do not assume power-associativity. We prove that if A admits a non-degenerate trace form, then A is a Jordan algebra. We also prove that if A is finite-dimensional and solvable, then it is nilpotent. We find three conditions, any of which implies that a finite-dimensional right-nilalgebra A is nilpotent.

Identifiers

DOI

10.1142/s1005386708000072

Citations and references