3 problems

The idempotent criterion conjecture. A subspace $M\subseteq V$ is a Mathieu–Zhao subspace of $V$ if and only if, whenever $e_i\in M$, one has $V^i\subseteq M$. This is proposed as…

Let $K$ be a field of characteristic $0$, let $\mathcal A$ be a $K$-algebra, and let $\delta$ be a locally nilpotent $K$-derivation or $K$-$\varepsilon$-derivation of $\mathcal A$.…

Let $\mathbb{C}[z]$ be a polynomial ring and let $\mathbb{D}[z]$ be the set of differential operators $\Phi$ of $\mathbb{C}[z]$ of the form … for some $h(z)\in\mathbb{C}[z]$ and…