Abstract The long-standing Auslander and Reiten Conjecture states that a finitely generated module over a finite-dimensional algebra is projective if certain Ext-groups vanish. Several authors, including Avramov, Buchweitz, Iyengar, Jorgensen, Nasseh, Sather-Wagstaff, and Şega, have studied a possible counterpart of the conjecture, or question, for commutative rings in terms of the vanishing of Tor. This has led to the notion of Tor-persistent rings. Our main result shows that the class of Tor-persistent local rings is closed under a number of standard procedures in ring theory.

中文翻译：

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在自 Tor 消失的模块上

摘要 长期存在的 Auslander 和 Reiten 猜想指出，如果某些 Ext 群消失，则有限维代数上的有限生成模块是射影的。包括 Avramov、Buchweitz、Iyengar、Jorgensen、Nasseh、Sather-Wagstaff 和 Şega 在内的几位作者，研究了根据 Tor 消失的交换环的猜想或问题的可能对应物。这导致了 Tor 持久环的概念。我们的主要结果表明，Tor 持久局部环类在环理论中的许多标准程序下是封闭的。