Abstract
Let Φbe an associative ring with 1, containing 1/6,and let A be an arbitrary Mal'tsev Φ-algebra. For some fully invariant ideals of an algebra A, we prove that their products lie in the annihilator Annof this algebra. As a consequence, it is inferred that for every algebra A over a field Φof characteristic 0, satisfying the nth Engel condition, there exists an N such that\(A^N \cdot A^2 \subseteq Ann^A \).Also, some identities in Mal'tsev algebras having faithful representations are proved to hold in separated Mal'tsev algebras; in the class of alternative algebras, new central and kernel functions are constructed.
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