2 problems

Let $R$ be a Cohen--Macaulay local ring, and let $\mathcal{X}$ be a resolving subcategory of $\operatorname{mod} R$. A module is maximal Cohen--Macaulay if its depth equals…

Let $R$ be a Cohen–Macaulay local ring. Let $\operatorname{\mathcal{X}}$ be a resolving subcategory of finitely generated $R$-modules with finite radius. Dao–Takahashi's conjecture…