Properties of cofinite modules and applications to local cohomology

1999 ◽  
Vol 125 (3) ◽  
pp. 417-423 ◽  
Author(s):  
LEIF MELKERSSON
Keyword(s):  
Local Cohomology ◽  
Cofinite Modules

scholarly journals Cofinite modules and local cohomology

1997 ◽  
Vol 121 (1) ◽  
pp. 45-52 ◽  
Author(s):  
Donatella Delfino ◽  
Thomas Marley
Keyword(s):  
Local Cohomology ◽  
Cofinite Modules

On Weakly Laskerian and Weakly Cofinite Modules

2012 ◽  
Vol 19 (04) ◽  
pp. 693-698
Author(s):  
Kazem Khashyarmanesh ◽  
M. Tamer Koşan ◽  
Serap Şahinkaya
Keyword(s):  
Local Ring ◽  
Noetherian Ring ◽  
Local Cohomology ◽  
Krull Dimension ◽  
Negative Integer ◽  
Finitely Generated ◽  
Local Cohomology Module ◽  
Commutative Noetherian Ring ◽  
Cofinite Modules ◽  
Gorenstein Local Ring

Let R be a commutative Noetherian ring with non-zero identity, 𝔞 an ideal of R and M a finitely generated R-module. We assume that N is a weakly Laskerian R-module and r is a non-negative integer such that the generalized local cohomology module [Formula: see text] is weakly Laskerian for all i < r. Then we prove that [Formula: see text] is also weakly Laskerian and so [Formula: see text] is finite. Moreover, we show that if s is a non-negative integer such that [Formula: see text] is weakly Laskerian for all i, j ≥ 0 with i ≤ s, then [Formula: see text] is weakly Laskerian for all i ≤ s and j ≥ 0. Also, over a Gorenstein local ring R of finite Krull dimension, we study the question when the socle of [Formula: see text] is weakly Laskerian?

Serre subcategories and the cofiniteness of generalized local cohomology modules with respect to a pair of ideals

2016 ◽  
Vol 26 (06) ◽  
pp. 1267-1282
Author(s):  
Tran Tuan Nam ◽  
Nguyen Minh Tri
Keyword(s):  
Local Cohomology ◽  
Cofinite Modules ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules ◽  
Serre Subcategories

We study some properties of the generalized local cohomology modules [Formula: see text] of [Formula: see text] with respect to a pair of ideals [Formula: see text] in Serre subcategories. Some results concerning to [Formula: see text]-cofinite modules are also given in this paper.

scholarly journals Artinianness of local cohomology modules

2014 ◽  
Vol 52 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Moharram Aghapournahr ◽  
Leif Melkersson
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Cohomology Modules

On the associated primes of local cohomology modules

1999 ◽  
Vol 27 (12) ◽  
pp. 6191-6198 ◽  
Author(s):  
K. Khashyarmanesh ◽  
Sh Salarian
Keyword(s):  
Local Cohomology ◽  
Associated Primes ◽  
Local Cohomology Modules ◽  
Cohomology Modules

scholarly journals Local cohomology of certain Rees- and form-rings, I

1983 ◽  
Vol 81 (1) ◽  
pp. 29-57 ◽  
Author(s):  
Markus Brodmann
Keyword(s):  
Local Cohomology
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