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.
Bass,On the ubiquity of Gorenstein rings, Math
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A survey of known results on the homological properties of noetherian Hopf algebras, with the central question remaining open after 30 years.
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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.
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Report on $AS$-Gorenstein Hopf algebras
A survey of known results on the homological properties of noetherian Hopf algebras, with the central question remaining open after 30 years.