On the Finiteness of Local Homology Modules
نویسندگان
چکیده
Let (R,m) be a commutative Noetherian complete local ring, a an ideal of R, and A an Artinian R-module with N-dim A = d. We prove that if d > 0, then Cosupp(H d−1(A)) is finite and if d ≤ 3, then the set Coass(H i (A)) is finite for all i. Moreover, if either d ≤ 2 or the cohomological dimension cd(a) = 1 then H i (A) is a-coartinian for all i; that is, Torj (R/a,H a i (A)) is Artinian for all i, j. We also show that if H a i (A) is a-coartinian for all i < n, then Torj (R/a,H a n (A)) is Artinian for j = 0,1. In particular, the set Coass(H a n (A)) is finite.
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