论文标题
关于在二维常规局部环上有限的Noetherian代数
On finite generation of Noetherian algebras over two-dimensional regular local rings
论文作者
论文摘要
让$ r $成为一个完全常规的本地环，带有代数封闭的残留场，让$ a $为多项式环$ r [x] $的noetherian $ r $ -subalgebra。在\ cite {do2}中已显示，如果$ \ dim r = 1 $，则$ a $必然在$ r $上有限生成。在本文中，当$ \ dim r = 2 $时，我们给出了$ a $的必要条件，以在$ r $上有限生成，并为$ r [x] $ of $ r [x] $ over $ r = {\ mathbb c} [\ mathbb c} [[u，v] $ of $ r [x] $的Noetherian普通产生的示例。
Let $R$ be a complete regular local ring with an algebraically closed residue field and let $A$ be a Noetherian $R$-subalgebra of the polynomial ring $R[X]$. It has been shown in \cite{DO2} that if $\dim R=1$, then $A$ is necessarily finitely generated over $R$. In this paper, we give necessary and sufficient conditions for $A$ to be finitely generated over $R$ when $\dim R=2$ and present an example of a Noetherian normal non-finitely generated $R$-subalgebra of $R[X]$ over $R= {\mathbb C}[[u, v]]$.
