Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4596001 | Journal of Pure and Applied Algebra | 2015 | 15 Pages |
Abstract
Let R be a local complete intersection ring and let M and N be nonzero finitely generated R -modules. We employ Auslander's transpose in the study of the vanishing of Tor and obtain useful bounds for the depth of the tensor product M⊗RNM⊗RN. An application of our main argument shows that, if M is locally free on the punctured spectrum of R , then either depth(M⊗RN)≥depth(M)+depth(N)−depth(R)depth(M⊗RN)≥depth(M)+depth(N)−depth(R), or depth(M⊗RN)≤codim(R)depth(M⊗RN)≤codim(R). Along the way we generalize an important theorem of D.A. Jorgensen and determine the number of consecutive vanishing of ToriR(M,N) required to ensure the vanishing of all higher ToriR(M,N).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Olgur Celikbas, Arash Sadeghi, Ryo Takahashi,