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Cofiniteness of Generalized Local Cohomology Modules for One-Dimensional Ideals |
Canad. Math. Bull. 55(2012), 81-87
Published:2011-03-21
Printed: Mar 2012
Printed: Mar 2012
- Kamran Divaani-Aazar,
- Alireza Hajikarimi,
Abstract
Let $\mathfrak a$ be an ideal of a commutative Noetherian
ring $R$ and $M$ and $N$ two finitely generated $R$-modules. Our
main result asserts that if $\dim R/\mathfrak a\leq 1$, then all generalized
local cohomology modules $H^i_{\mathfrak a}(M,N)$ are $\mathfrak a$-cofinite.
| Keywords: | cofinite modules, generalized local cohomology modules, local cohomology modules |
| MSC Classifications: |
13D45 - Local cohomology [See also 14B15] 13E05 - Noetherian rings and modules 13E10 - Artinian rings and modules, finite-dimensional algebras |