7 problems

Let $K$ be a field, let $n\geq 2$, and let $D$ be a simple derivation of the polynomial ring $K[x_1,\ldots,x_n]$. A $K$-subspace $M$ of a ring is a Mathieu-Zhao space if, whenever…

Let $K$ be the algebraically closed field of characteristic zero fixed in the paper, and let $\delta=I-\phi$ be an E-derivation of $K[x_1,x_2,x_3]$, where, for $i=1,2$,…

Let $K$ be a field of characteristic zero, let $\mathcal{A}$ be a $K$-algebra, and let $\delta$ be a locally nilpotent derivation or E-derivation of $\mathcal{A}$. A $\vartheta$-id…

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 $M$…

LNED conjecture. Let $K$ be a field of characteristic zero, let $\mathcal{A}$ be a $K$-algebra, and let $\delta$ be a locally nilpotent derivation or $\mathcal{E}$-derivation of…

LFED conjecture. Let $K$ be a field of characteristic zero and $\mathcal{A}$ a $K$-algebra. Then for every locally finite derivation or $\mathcal{E}$-derivation $\delta$ of…

Let $X=(X_1,\dots,X_n)$ be a random vector with independent centered, variance-one Gaussian components. Let … A subspace $V$ is an MZ space if $f^m\in V$ for all $m\geq1$ implies…