Filtrations of Totally Reflexive Modules

Denise A. Rangel Tracy

Abstract: In this paper, we will introduce a subcategory of totally reflexive modules that have a saturated filtration by other totally reflexive modules. We will prove these are precisely the totally reflexive modules with an upper-triangular presentation matrix. We conclude with an investigation of the ranks of $\operatorname{Ext}^1$ of two such modules over a specific ring.

ArXiv: 1410.0732