Abstract

When a commutative nilalgebra has nilidex four, we can separate their study in three big cases. One of them is when the algebra A satisfies the identity (((yx)x)x)x = 0. In this paper we get results on the structure of this kind of algebras. Let W be the subspace of A generated by the cubes. We prove that W-2 = 0 and we use this to get others properties of W.