A generalization of the Auslander–Buchsbaum formula Original Research Article

Let R be a local ring, and let M and N be nonzero finitely generated R-modules. In this paper we demonstrate the equalityimagesup{iToriR(M,N)≠0}=sup{depth Rp−depth Mp−depth Nppset membership, variantsupp M∩supp N},provided eitherimage