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• # Artykuł - szczegóły

## Colloquium Mathematicum

2014 | 136 | 2 | 221-230

## Cofiniteness of torsion functors of cofinite modules

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.

221-230

wydano
2014

### Twórcy

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