Abstract
Let ϕ be an associative commutative ring with unity containing 1/6. Let A and B be a free Mal’tsev and a free alternative ϕ-algebras on a set of k≥6 free generators, respectively. We construct nonzero homogeneous elements of degree 7 belonging to an annihilatorAnnA of A, and nonzero homogeneous elements of degree 7 belonging to the center Z(B) of B. It is shown that a nilpotent Mal’tsev algebra of index 8 on a set of 6 generators has no faithful representation.
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