2 problems

Let $c$ be a positive integer. Let $\mathbf{M}$ be a finitely generated $\operatorname{OI}$-module over $\mathbf{P}=({\mathbf{X}}^{\operatorname{OI},1})^{\otimes c}$, or a finitely…

Let $c$ be a positive integer. Let $\mathbf{M}$ be a finitely generated graded $\operatorname{OI}$-module over $\mathbf{P}=({\mathbf{X}}^{\operatorname{OI},1})^{\otimes c}$, or a f…