Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588937 | Journal of Algebra | 2006 | 14 Pages |
Abstract
It 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory