Cofiniteness of torsion functors of cofinite modules

• Autorzy: Reza Naghipour , Kamal Bahmanpour , Imaneh Khalili Gorji
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 14B15: Local cohomology
• 13E05: Noetherian rings and modules
• 13D45: Local cohomology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 136
• Numer: 2
• Strony: 221-230

Daty

wydano

2014

Twórcy

autor

Reza Naghipour

• Department of Mathematics, University of Tabriz, Tabriz, Iran
• School of Mathematics, Institute for Research, in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

autor

Kamal Bahmanpour

• Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran
• School of Mathematics, Institute for Research, in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

autor

Imaneh Khalili Gorji

• Department of Basic Sciences, Imam Khomeini International University, P.O. Box 34149-1-6818, Qazvin, Iran

Identyfikatory

DOI

10.4064/cm136-2-4