Kronecker factorization theorems for the exceptional Malcev algebra

In this paper, we prove that a Malcev algebra [Formula: see text] that belongs to a certain variety of Malcev algebras [Formula: see text] such that [Formula: see text] contains the seven-dimensional exceptional Malcev algebra [Formula: see text] is isomorphic to a direct sum [Formula: see text], where [Formula: see text] is an associative commutative algebra. Also, we prove that a Malcev superalgebra [Formula: see text] in [Formula: see text] whose even part [Formula: see text] contains [Formula: see text] is isomorphic to a direct sum [Formula: see text], where [Formula: see text] is an associative supercommutative superalgebra.