Images of Locally Finite Derivations of Polynomial Algebras in Two Variables

Details Images of Locally Finite Derivations of Polynomial Algebras in Two Variables Images of Locally Finite Derivations of Polynomial Algebras in Two Variables

2010-04-04

arxiv.org/abs/1004.0521v2

Mathematics

Commutative Algebra

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

Scientific paper

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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