Free Malcev superalgebra on one odd generator and related superalgebras

A base of the universal multiplicative envelope of the free Malcev superalgebra $\mathcal M$ on one odd generator is constructed. Some corollaries for skew-symmetric functions and central elements in free Malcev and free alternative algebras are obtained. Moreover, a base of the Poisson–Malcev superalgebra of $\mathcal M$ is constructed. As a corollary, a set of elements that spans the free alternative superalgebra on one odd generator is obtained.