2 problems

Let $R$ be a non-Gorenstein local ring. A finitely generated $R$-module is totally reflexive if it has G-dimension zero. Infinitely many indecomposable totally reflexive modules co…

Let $R$ be the local ring under consideration, let $B$ be an $R$-module with $operatorname{depth}R B<infty$, and let $M$ range over all totally reflexive $R$-modules. Tensor-depth…