2 problems

Let $R$ be the ring under consideration, let $C$ be a semidualizing module, and let $X$ be any $R$-module. Write $\mathcal{G}_C\mathop{\rm \text{-}\dim}\nolimits X$ and…

Let $R$ be a local $k$-algebra such that the $R$-module of $k$-derivations $\operatorname{Der}_k(R)$ is finitely generated. Write $\operatorname{Gdim}$ for Gorenstein dimension and…