# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Cofiniteness of generalized local cohomology modules

### Tom 99 / 2004

Colloquium Mathematicum 99 (2004), 283-290 MSC: 13D45, 14B15. DOI: 10.4064/cm99-2-12

#### Streszczenie

Let ${\mathfrak a}$ denote an ideal of a commutative Noetherian ring $R$, and $M$ and $N$ two finitely generated $R$-modules with $\mathop{\rm pd} M< \infty$. It is shown that if either ${\mathfrak a}$ is principal, or $R$ is complete local and ${\mathfrak a}$ is a prime ideal with $\dim R/{\mathfrak a}=1$, then the generalized local cohomology module $H^i_{{\mathfrak a}}(M,N)$ is $\mathfrak a$-cofinite for all $i \geq 0$. This provides an affirmative answer to a question proposed in [{13}].

#### Autorzy

• Kamran Divaani-AazarDepartment of Mathematics
Az-Zahra University, Vanak
Tehran 19834, Iran
and Institute for Studies
in Theoretical Physics and Mathematics
P.O. Box 19395-5746, Tehran, Iran
e-mail
• Reza SazeedehDepartment of Mathematics
Uromeiyeh University
Uromeiyeh, Iran
and
Institute of Mathematics
University for Teacher Education
599 Taleghani Avenue
Tehran 15614, Iran

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