Abstract Given a noetherian ring R and n ≥ 2 , it is well-known that residual coordinates of the polynomial algebra R [ n ] are m-stable coordinates for some m ≥ 1 , that is they become coordinates in the larger polynomial algebra R [ n + m ] . In this paper we prove that, over a large class of noetherian one-dimensional rings, m = 1 is enough. This includes affine algebras over an algebraically closed field as well as noetherian complete local rings containing a field.

中文翻译：

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一维环上的残差坐标

摘要 给定一个诺特环 R 和 n ≥ 2 ，众所周知多项式代数 R [ n ] 的残差坐标对于某些 m ≥ 1 是 m 稳定坐标，即它们成为更大多项式代数 R [ n+m]。在本文中，我们证明，在一大类诺特一维环上，m = 1 就足够了。这包括代数闭域上的仿射代数以及包含域的诺特完全局部环。