  We consider three types of rings of supersymmetric polynomials: polynomial
ones $\Lambda_{m,n}$, partially polynomial $\Lambda_{m,n}^{+y}$ and Laurent
supersymmetric rings $\Lambda_{m,n}^{\pm}$. For each type of rings we give
their descriptions in terms of generators and relations. As a corollary we get
for $n\ge m$ an isomorphism
$\Lambda_{m,n}^{+y}=\Lambda_{m,m}^{+y}\otimes\Lambda^{+y}_{0,n-m}$. We also
have the same sort of isomorphism for polynomial rings, but in this case the
isomorphism does not preserve the grading. For each type of rings we also
construct some natural basis consisting of Euler characters.
