Socle of a quotient of the ring of differential operators of a polynomial ring

I have been reading the following paper: https://www.sciencedirect.com/science/article/pii/S002240491000263X

Proposition 2.4(ii) shows that if $$\mathfrak D$$ is a ring of $$k$$-linear differential operators of the polynomial ring $$R=k[x_1, \cdots , x_n]$$, then for every $$k$$-rational maximal ideal $$\mathfrak m$$ of $$R$$ (i.e. a maximal ideal $$\mathfrak m \vartriangleleft R$$ for which the canonical map $$k \rightarrow R/\mathfrak m$$ is an isomorphism), the socle of $$\mathfrak D/\mathfrak D \mathfrak m$$ is generated by $$\overline 1$$. There is a part in the proof in this proposition which reads that in order to demonstrate this assertion, "It remains to show that every non-zero element $$z$$ can be sent to $$1$$ by an element of $$R$$."

I am not sure why at that point in the proof, this is sufficient to show the desired assertion on the socle of $$\mathfrak D/\mathfrak D \mathfrak m$$. The only definitions of socle in this (non-local) scenario that I am aware of are that the socle is the sum of simple submodules or equivalently the intersection of all essential submodules (and that is basically all I know about the socle, so I apologize for the possible naivete of the question) and I can't seem to be able to correlate what either of these two definitions has to do with the sufficiency claimed above. I would really appreciate any help or reference here, thank you.