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arXiv · 1004.0521

Images of Locally Finite Derivations of Polynomial Algebras in Two Variables

Arno van den Essen·David Wright·Wenhua Zhao
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Abstract

In this paper we show that the image of any locally finite $k$-derivation of the polynomial algebra $k[x, y]$ in two variables over a field $k$ of characteristic zero is a Mathieu subspace. We also show that the two-dimensional Jacobian conjecture is equivalent to the statement that the image $Im D$ of every $k$-derivation $D$ of $k[x, y]$ such that $1\in Im D$ and $div D=0$ is a Mathieu subspace of $k[x, y]$.

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BibTeXRIS

Arno van den Essen, David Wright, Wenhua Zhao. 2010-04-04. Images of Locally Finite Derivations of Polynomial Algebras in Two Variables. https://arxiv.org/abs/1004.0521

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