The Tor Game
نویسندگان
چکیده
Let M and N be non-zero finitely generated modules over a local (Noetherian) ring (R,m). Assume that TorRi (M,N) = 0 for i >> 0, and let q = qR(M,N) be the largest integer i for which TorRi (M,N) 6= 0. For the case q = 0, Auslander [A, Theorem 1.2] found a useful formula relating the depths of M , N and R. In view of the Auslander-Buchsbaum formula [BH,Thm. 1.3.3] Auslander’s theorem goes as follows:
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