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 whichStanley-Reisner rings of graphs admit non-free totally reflexive modules.
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机译：对于标准等级的Cohen-Macaulay Ring $ S $，如果商/（ Underline {x}）$允许不自由的完全反身，其中$ 下划线{x} $是由元素组成的参数系统一个学位，那么戒指$ S $。作为一个应用程序，我们考虑到TheTanley-Reisner的问题的问题，图形响应了无防免完全反射模块。
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