The Image Conjecture for regular sequences

Let $k$ be a field and $A$ be a $k$-algebra, and let $B=A[z_1,\ldots,z_n]$ be the polynomial ring in $n$ variables over $A$. For $a_1,\ldots,a_n\in A$ a regular sequence means a sequence satisfying the usual non-zero-divisor and proper-ideal conditions. Let $\mathcal D:B^n\to B$ be the $A$-linear map whose components are $\partial_{z_i}-a_i$.

Image Conjecture. The image of $\mathcal D$ is a Mathieu subspace of $B$.

This conjecture generalizes the ideal-like behavior of images of differential operators and is connected with the Vanishing and Jacobian Conjectures. The source presents it as the main conjecture and does not give evidence here that it has been resolved.