On a Depth Formula for Modules over Local Rings
نویسندگان
چکیده
We prove that for modules M and N over a local ring R, the depth formula: depthR M + depthR N − depthR = depthR Tor R s (M,N) − s, where s = sup{i | Tor i (M,N) 6= 0}, holds under certain conditions. This adds to the list cases where the depth formula, which extends the classical Auslander-Buchsbaum equality, is satisfied.
منابع مشابه
Vanishing of Tate Homology and Depth Formulas over Local Rings
Auslander’s depth formula for pairs of Tor-independent modules over a regular local ring, depth(M ⊗R N) = depth M + depth N − depthR, has been generalized in several directions; most significantly it has been shown to hold for pairs of Tor-independent modules over complete intersection rings. In this paper we establish a depth formula that holds for every pair of Tate Tor-independent modules ov...
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