论文标题
$ b（x，y）z^n-a（x，y）$的飞机上的dvr
Planes of the form $b(X,Y)Z^n-a(X,Y)$ over a DVR
论文作者
论文摘要
在本文中，我们将D. Wright的表达定理扩展到了离散估值环的情况。我们将证明，如果$（r，t）$是一个离散的估值戒指，$ n \ ge 2 $是一个整数，则不可能由残基字段$ r/tr $的特征和$ g \ in R [x，y，z] $在$ g = b（x，y）z^n -y（x，x，y）$ g py y [x，y，z]中的特征上，y y y y y y y y y y y y y y y x y y [x，y）$ r [代数为两个变量，然后$ g $和$ z $形成$ r [x，y，z] $的变量。我们还将证明该结果始于包含$ \ mathbb {q} $的任何Noetherian域。
In this paper we extend an epimorphism theorem of D. Wright to the case of discrete valuation rings. We will show that if $(R, t)$ is a discrete valuation ring, $n \ge 2$ is an integer not divisible by the characteristic of the residue field $R/tR$, and $g \in R[X, Y, Z]$ is a polynomial of the form $g = b(X,Y)Z^n - a(X,Y)$ such that $R[X, Y, Z]/(g)$ is a polynomial algebra in two variables, then $g$ and $Z$ form a pair of variables in $R[X, Y, Z]$. We will also show that the result holds over any Noetherian domain containing $\mathbb{Q}$.
