Images of Locally Finite Derivations of Polynomial Algebras in Two Variables
Images of Locally Finite Derivations of Polynomial Algebras in Two Variables
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DOI：
10.1016/j.jpaa.2010.12.002
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发表时间：
2010-04
期刊：
影响因子：
3.7
通讯作者：
A. Essen;D. Wright;Wenhua Zhao
中科院分区：
文献类型：
--
作者：
A. Essen;D. Wright;Wenhua Zhao
本文证明了特征为零的域k上二元多项式代数k[x，y]的任何局部有限k-导子的象是Mathieu子空间。证明了二维Jacobian猜想等价于k[x，y]的每个k-导子D的象ImD是k [x，y]的Mathieu子空间，使得1∈ImD且div D=0.
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∈ImD and div D=0 is a Mathieu subspace of k[x,y].