Cofiniteness of torsion functors of cofinite modules

Reza Naghipour ; Kamal Bahmanpour ; Imaneh Khalili Gorji

Colloquium Mathematicae, Tome 135 (2014), p. 221-230 / Harvested from The Polish Digital Mathematics Library

Résumé

Let R be a Noetherian ring and I an ideal of R. Let M be an I-cofinite and N a finitely generated R-module. It is shown that the R-modules $Tor_{i}^{R}(N,M)$ are I-cofinite for all i ≥ 0 whenever dim Supp(M) ≤ 1 or dim Supp(N) ≤ 2. This immediately implies that if I has dimension one (i.e., dim R/I = 1) then the R-modules $Tor_{i}^{R}(N,H^{j}_{I}(M))$ are I-cofinite for all i,j ≥ 0. Also, we prove that if R is local, then the R-modules $Tor_{i}^{R}(N,M)$ are I-weakly cofinite for all i ≥ 0 whenever dim Supp(M) ≤ 2 or dim Supp(N) ≤ 3. Finally, it is shown that the R-modules $Tor_{i}^{R}(N,H^{j}_{I}(M))$ are I-weakly cofinite for all i,j ≥ 0 whenever dim R/I ≤ 2.

Détail

Publié le : 2014-01-01

Zbl 1306.13012

EUDML-ID : urn:eudml:doc:283503