Cofiniteness of torsion functors of cofinite modules

Reza Naghipour, Kamal Bahmanpour, and Imaneh Khalili Gorji. "Cofiniteness of torsion functors of cofinite modules." Colloquium Mathematicae 136.2 (2014): 221-230. <http://eudml.org/doc/283503>.

@article{RezaNaghipour2014,
abstract = {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.},
author = {Reza Naghipour, Kamal Bahmanpour, Imaneh Khalili Gorji},
journal = {Colloquium Mathematicae},
keywords = {Cofinite; local cohomology; weakly cofinite; weakly Laskerian},
language = {eng},
number = {2},
pages = {221-230},
title = {Cofiniteness of torsion functors of cofinite modules},
url = {http://eudml.org/doc/283503},
volume = {136},
year = {2014},
}

TY - JOUR
AU - Reza Naghipour
AU - Kamal Bahmanpour
AU - Imaneh Khalili Gorji
TI - Cofiniteness of torsion functors of cofinite modules
JO - Colloquium Mathematicae
PY - 2014
VL - 136
IS - 2
SP - 221
EP - 230
AB - 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.
LA - eng
KW - Cofinite; local cohomology; weakly cofinite; weakly Laskerian
UR - http://eudml.org/doc/283503
ER -