Images of Locally Finite Derivations of Polynomial Algebras in Two Variables

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 $ImD$ of every $k$-derivation $D$ of $k[x,y]$ such that $1\in ImD$ and $divD=0$ is a Mathieu subspace of $k[x,y]$.

arXiv commentMinor changes and improvements. Latex, 9 pages. To appear in J. Pure Appl. Algebra

References in corpus (1)

• Some Results on the Vanishing Conjecture of Differential Operators with Constant Coefficients

Cited by in corpus (1)

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