 that ${\overline{{\mathbb F}}_{\hskip-0.0mm q}}[A_{r-0} {\ifm {,\ldots,} {$,\ldots,$}}A_0]/(L_0 {\ifm {,\ldots,} {$,\ldots,$}}L_m) \simeq {\overline{{\mathbb F}}_{\hskip-0.0mm q}}[A_k: k \in \mathcal{J}]$ 