Brauer-Thrall for totally reflexive modules over local rings of higher dimension

Olgur Celikbas, Mohsen Gheibi, Ryo Takahashi

Let $R$ be a commutative Noetherian local ring. Assume that $R$ has a pair $\{x,y\}$ of exact zerodivisors such that $\dim R/(x,y)\ge 2$ and all totally reflexive $R/(x)$-modules ar…