  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 \c{S}ega, have studied a possible
counterpart of the conjecture, or question, for commutative rings in terms of
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.
