Nilpotency of commutative finitely generated algebras satisfying L(x)(3) + gamma L(x)(3)=0, gamma=1, 0

Abstract

This paper deals with two varieties of commutative non-associative algebras. One variety satisfies L(x)(3) + L(x)(3) = 0. The other variety satisfies L(x)(3) = 0. We prove that in either variety, any finitely generated algebra is nilpotent. Our results require characteristic not equal 2, 3. (C) 2010 Elsevier Inc. All rights reserved.