Speciality of Malcev superalgebras on one odd generator

AbstractIt is proved that every Malcev superalgebra generated by an odd element is special, that is, isomorphic to a subsuperalgebra of the commutator Malcev superalgebra A− for a certain alternative superalgebra A. As a corollary, it is shown that the kernel of the natural homomorphism of the free Malcev algebra Malc[X] of countable rank into the commutator Malcev algebra Alt[X]− of the corresponding free alternative algebra Alt[X], does not contain skew-symmetric multilinear elements. In other words, there are no skew-symmetric Malcev s-identities. Another corollary is speciality of the Malcev Grassmann algebra