scholarly journals Finiteness properties of local cohomology modules for $\mathfrak a$-minimax modules

2008 ◽  
Vol 137 (02) ◽  
pp. 439-448 ◽  
Author(s):  
Jafar Azami ◽  
Reza Naghipour ◽  
Bahram Vakili
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Minimax Modules ◽  
Finiteness Properties ◽  
Cohomology Modules

Minimax modules, local homology and local cohomology

2015 ◽  
Vol 26 (12) ◽  
pp. 1550102 ◽  
Author(s):  
Tran Tuan Nam
Keyword(s):  
Local Cohomology ◽  
Local Homology ◽  
Local Cohomology Modules ◽  
Minimax Modules ◽  
Equivalent Properties ◽  
Cohomology Modules

We show some results about local homology modules and local cohomology modules concerning Grothendieck’s conjecture and Huneke’s question. We also show some equivalent properties of [Formula: see text]-separated modules and of minimax local homology modules. By duality, we get some properties of Grothendieck’s local cohomology modules.

Matlis Duality and Finiteness Properties of Generalized Local Cohomology Modules

2010 ◽  
Vol 17 (04) ◽  
pp. 637-646 ◽  
Author(s):  
Hero Saremi
Keyword(s):  
Local Cohomology ◽  
Projective Dimension ◽  
Regular Sequence ◽  
Local Cohomology Module ◽  
Local Cohomology Modules ◽  
Matlis Duality ◽  
Noetherian Dimension ◽  
Generalized Local Cohomology Modules ◽  
Finiteness Properties ◽  
Cohomology Modules

Let [Formula: see text] be an ideal of a commutative Noetherian local ring [Formula: see text] and M, N be two finitely generated R-modules such that M is of finite projective dimension n. Let t be a positive integer. We show that if there exists a regular sequence [Formula: see text] with [Formula: see text] and the i-th local cohomology module [Formula: see text] of N with respect to [Formula: see text] is zero for all i > t, then [Formula: see text], where D(-):= Hom R(-,E). Also, we prove that if N is a Cohen-Macaulay R-module of dimension d, then the generalized local cohomology module [Formula: see text] is co-Cohen-Macaulay of Noetherian dimension d. Finally, with an elementary proof, we show that [Formula: see text] is finite.

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