# Cofiniteness of torsion functors of cofinite modules

Reza Naghipour; Kamal Bahmanpour; Imaneh Khalili Gorji

Colloquium Mathematicae (2014)

- Volume: 136, Issue: 2, page 221-230
- ISSN: 0010-1354

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topReza 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 -

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