2 results
Cofiniteness of Generalized Local Cohomology Modules for One-Dimensional Ideals
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- Journal:
- Canadian Mathematical Bulletin / Volume 55 / Issue 1 / 01 March 2012
- Published online by Cambridge University Press:
- 20 November 2018, pp. 81-87
- Print publication:
- 01 March 2012
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- Article
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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 
$R/\mathfrak{a}\,\le \,1$, then all generalized local cohomology modules 
$H_{\mathfrak{a}}^{i}(M,\,N)$ are $\mathfrak{a}$-cofinite.
ATTACHED PRIMES OF THE TOP GENERALIZED LOCAL COHOMOLOGY MODULES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 79 / Issue 1 / February 2009
- Published online by Cambridge University Press:
- 10 March 2009, pp. 59-67
- Print publication:
- February 2009
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Let (R,𝔪) be a commutative Noetherian local ring, let I be an ideal of R and let M and N be finitely generated R-modules. Assume that
, 
. First, we give the formula for the attached primes of the top generalized local cohomology module HId+n(M,N); later, we prove that if Att(HId+n(M,N))=Att(HJd+n(M,N)), then HId+n(M,N)=HJd+n(M,N).
, 
. First, we give the formula for the attached primes of the top generalized local cohomology module 