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Cofiniteness of torsion functors of cofinite modules

100%

Naghipour R., Bahmanpour K., Gorji I.

Colloquium Mathematicum

2014

tom 136

nr 2

221-230

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.

Upper bounds for the cohomological dimensions of finitely generated modules over a commutative Noetherian ring

100%

Ghasemi G., Bahmanpour K., A'zami J.

Colloquium Mathematicum

2014

tom 137

nr 2

263-270

Let R be a commutative Noetherian ring, I a proper ideal of R, and M be a finitely generated R-module. We provide bounds for the cohomological dimension of the R-module M with respect to the ideal I in several cases.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Bahmanpour K.

1 A'zami J.

1 Ghasemi G.

1 Gorji I.

1 Naghipour R.

2 2014

Wyniki wyszukiwania

Cofiniteness of torsion functors of cofinite modules

Upper bounds for the cohomological dimensions of finitely generated modules over a commutative Noetherian ring