主理想域上的通用两变量坐标系

Pub Date : 2024-06-19 DOI:10.1007/s00031-024-09862-3

M’hammed El Kahoui, Najoua Essamaoui, Miloud Ez-zinbi

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引用次数: 0

摘要

让 \(R\) 是一个主理想域。本文将研究多项式 \(R\)- 代数 \(A=R^{[2]}\) 的一般坐标系。作为应用，我们证明了对于每一个局部零potent \(R\)-derivation \(\xi \) of \(A\) 的自动形 \(\exp (\xi )\) 在 \(A\) 的适当坐标系中都是 1 稳定驯服的。这就表明，由史密斯（Smith）提出的、断言长田自形为1-稳定驯服的著名结果实际上在一般情况下是完全成立的。

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Generic Coordinate Systems in Two Variables Over a Principal Ideal Domain

Let \(R\) be a principal ideal domain. In this paper we investigate generic coordinate systems of the polynomial \(R\)-algebra \(A=R^{[2]}\). As an application we prove that for every locally nilpotent \(R\)-derivation \(\xi \) of \(A\) the automorphism \(\exp (\xi )\) is 1-stably tame in an appropriate coordinate system of \(A\). This shows that the well-known result due to Smith, asserting that the Nagata automorphism is 1-stably tame, actually holds in full generality.

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