For Cohen-Macaulay local rings, the left and right depth formula conditions are characterized by the Uniform Auslander Condition and a newly introduced Uniform Buchweitz Condition, respectively.
Algebras that satisfy A uslander's condition on vanishing of cohomology
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On the depth of tensor products over Cohen-Macaulay rings
For Cohen-Macaulay local rings, the left and right depth formula conditions are characterized by the Uniform Auslander Condition and a newly introduced Uniform Buchweitz Condition, respectively.