论文标题
本地有限$ \ Mathcal {e} $的图像 - 双变量多项式代数的衍生
Images of locally finite $\mathcal{E}$-derivations of bivariate polynomial algebras
论文作者
论文摘要
本文介绍了$ \ Mathcal {e} $ - 由于范登·埃森（Van den Essen），赖特（Wright）和赵（Zhao）引起的衍生结果的衍生类似物。我们证明，本地有限$ K $ - $ \ MATHCAL {e} $ - 多项式代数在两个变量的特征零的字段$ k $中的衍生是Mathieu-Zhao子空间。这一结果与范登·埃森（Van den Essen）一起，赖特（Wright）和赵（Zhao）在两个变量中多项式代数的情况下证实了LFED的猜想。
This paper presents an $\mathcal{E}$-derivation analogue of a result on derivations due to van den Essen, Wright and Zhao. We prove that the image of a locally finite $K$-$\mathcal{E}$-derivation of polynomial algebras in two variables over a field $K$ of characteristic zero is a Mathieu-Zhao subspace. This result together with that of van den Essen, Wright and Zhao confirms the LFED conjecture in the case of polynomial algebras in two variables.
