论文标题
算术环的度数
A degree bound for rings of arithmetic invariants
论文作者
论文摘要
考虑一个Noetherian域$ r $和有限的组$ g \ subseteq gl_n（r）$。我们证明，如果不变的环$ r [x_1，\ ldots，x_n]^g $是cohen-macaulay戒指，那么它将以$ r $ -Algebra的形式生成$ r $ -Algebra，该元素最多是$ \ max（| g |，n（| g | -1））$。作为中级结果，我们还表明，如果$ r $是具有无限残留场的Noetherian本地戒指，那么这样的有限组$ g $ i $ r $的不变式戒指包含一个均质的参数系统，该参数最多包含$ | g | $的元素。
Consider a Noetherian domain $R$ and a finite group $G \subseteq Gl_n(R)$. We prove that if the ring of invariants $R[x_1, \ldots, x_n]^G$ is a Cohen-Macaulay ring, then it is generated as an $R$-algebra by elements of degree at most $\max(|G|,n(|G|-1))$. As an intermediate result we also show that if $R$ is a Noetherian local ring with infinite residue field then such a ring of invariants of a finite group $G$ over $R$ contains a homogeneous system of parameters consisting of elements of degree at most $|G|$.
