Let $A$ be a Gorenstein and seminormal $\mathbb{C}$-algebra of finite type, and let $t \in A$ be some non-zero divisor.
If $M$ is a finitely generated $A$-module, and $t$ is an $M$-regular element, is $t$ then an $ \operatorname{Ext}^1_A(M,A)$-regular element?
One can equivalently formulate this question as such:
If $T : A^{\oplus n} \to A^{\oplus m}$ is a linear map such that $tx \in \operatorname{Im}(T) \Rightarrow x \in \operatorname{Im}(T)$ for all $x \in A^{\oplus m}$, does the same hold for its transpose $T^t : A^{\oplus m} \to A^{\oplus n}$? Here $n$ and $m$ are arbitrary integers.