关于超对称多项式环
On rings of supersymmetric polynomials
摘要：
我们考虑三种类型的超对称多项式环：多项式环$Λ_{m,n}$，部分多项式环$Λ_{m,n}^{+y}$和Laurent超对称环$Λ_{m,n}^{\pm}$ .对于每种类型的环，我们给出了它们的描述的生成元和关系。作为推论，我们得到$n\ge m$的同构$Λ_{m,n}^{+y}=Λ_{m,m}^{+y}\otimesΛ^{+y}_{0,n-m}$。对于多项式环，我们也有同样的同构，但在这种情况下，同构不保持分次。对于每一种类型的环，我们还构造了一些自然基组成的欧拉特征标。
英文摘要：
We consider three types of rings of supersymmetric polynomials: polynomial ones $Λ_{m,n}$, partially polynomial $Λ_{m,n}^{+y}$ and Laurent supersymmetric rings $Λ_{m,n}^{\pm}$. 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 $Λ_{m,n}^{+y}=Λ_{m,m}^{+y}\otimesΛ^{+y}_{0,n-m}$. 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.
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