A base of the free alternative superalgebra on one odd generator is constructed. As a corollary, a base of the alternative Grassmann algebra is given. We also find a new element of degree 5 from the radical of the free alternative algebra of countable rank.
Communicated by M. Sapir MSC: Primary: 17D05 17A45 secondary: 17A70 17A75 a b s t r a c t Quadratic alternative superalgebras are introduced and their super-identities and central functions on one odd generator are described. As a corollary, all multilinear skewsymmetric identities and central polynomials of octonions are classified.
A base of the Malcev Poisson superalgebra related with the free Malcev superalgebra on one odd generator is constructed. As a corollary, a pre-base, that is, a set of elements that spans the free alternative superalgebra on one odd generator is obtained.
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