The LFED conjecture for locally finite derivations and E-derivations

Let $K$ be a field of characteristic zero, let $\mathcal{A}$ be a $K$-algebra, and let $\delta$ be a locally finite derivation or E-derivation of $\mathcal{A}$. A $K$-subspace $M$ of $\mathcal{A}$ is a Mathieu-Zhao space if, whenever $a\in\mathfrak{r}(M)$, one has $ba^m\in M$ for all sufficiently large $m$ and every $b\in\mathcal{A}$, where $\mathfrak{r}(M)=\{a\in\mathcal{A}:a^m\in M\text{ for all sufficiently large }m\}$. LFED conjecture. The image $\operatorname{Im}\delta:=\delta(\mathcal{A})$ is a Mathieu-Zhao space of $\mathcal{A}$. This conjecture, posed by Wenhua Zhao, concerns the Mathieu-Zhao property of images of locally finite derivations and E-derivations; its resolution is not specified in the supplied text.