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arXiv · 1602.08385

On the existence of non-free totally reflexive modules

Cameron Atkins·Adela Vraciu
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Abstract

For a standard graded Cohen-Macaulay ring $S$, if the quotient $S/(\underline{x})$ admits non-free totally reflexive modules, where $\underline{x}$ is a system of parameters consisting of elements of degree one, then so does the ring $S$. As an application, we consider the question of which Stanley-Reisner rings of graphs admit non-free totally reflexive modules.

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Cameron Atkins, Adela Vraciu. 2016-02-26. On the existence of non-free totally reflexive modules. https://arxiv.org/abs/1602.08385

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