论文标题
某些$ \ mathcal {e} $ - 派生的LFED猜想
The LFED Conjecture for some $\mathcal{E}$-derivations
论文作者
论文摘要
令$ k $为特征零的代数封闭字段，$δ$ a nonzero $ \ mathcal {e} $ - $ k [x] $的推导。我们首先证明$ \ operatorname {im}δ$在某些情况下是$ k [x] $的Mathieu-Zhao空间。然后，我们证明了所有$δ= i-ϕ $的LFED猜想是正确的，其中$ ϕ $是$ K [x_1，x_2] $的仿射多项式同构。最后，我们证明，对于$ k的一些$δ$ [x_1，x_2，x_3] $，LFED的猜想是正确的。
Let $K$ be an algebraically closed field of characteristic zero, $δ$ a nonzero $\mathcal{E}$-derivation of $K[x]$. We first prove that $\operatorname{Im}δ$ is a Mathieu-Zhao space of $K[x]$ in some cases. Then we prove that LFED Conjecture is true for all $δ=I-ϕ$, where $ϕ$ is an affine polynomial homomorphism of $K[x_1,x_2]$. Finally, we prove that LFED Conjecture is true for some $δ$ of $K[x_1,x_2,x_3]$.
