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Abstract
We prove that for modules M and N over a local ring R, the depth formula: depth R M + depth R N − depth R = depth R Tor s R (M, N) − s, where s = sup{i∣Tor i R (M, N) ≠ 0}, holds under certain conditions. This adds to the list cases where the depth formula, which extends the classical Auslander-Buchsbaum equality, is satisfied.
ACKNOWLEDGMENTS
This collaboration owes its existence to Luchezar Avramov and Craig Huneke, who made each of us aware of the other's work. It is a pleasure to thank them for the same and for their encouragement. Our thanks also to David Jorgensen for his valuable remarks on an earlier version of this paper.