Modules with finite projective dimension over local rings are frequently forced to be free when their self-tensor products satisfy torsion-freeness or reflexivity, extending Auslander's classical results.
Seydi,Anneaux Henseliens et condition de chaine III, Bull
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Remarks on modules of finite projective dimension
Modules with finite projective dimension over local rings are frequently forced to be free when their self-tensor products satisfy torsion-freeness or reflexivity, extending Auslander's classical results.