On the finiteness properties of associated primes of generalized local cohomology modules

2008 ◽  
Vol 20 (2) ◽  
Author(s):  
Kazem Khashyarmanesh
Keyword(s):  
Local Cohomology ◽  
Associated Primes ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Finiteness Properties ◽  
Cohomology Modules

scholarly journals On the asymptotic behaviour of associated primes of generalized local cohomology modules

2007 ◽  
Vol 83 (2) ◽  
pp. 217-226 ◽  
Author(s):  
Kazem Khashyarmaneshs ◽  
Ahmad Abbasi
Keyword(s):  
Asymptotic Behavior ◽  
Local Cohomology ◽  
Associated Primes ◽  
Finitely Generated ◽  
Local Cohomology Module ◽  
Commutative Noetherian Ring ◽  
Graded Modules ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules

AbstractLetMandNbe finitely generated and graded modules over a standard positive graded commutative Noetherian ringR, with irrelevant idealR+. Letbe thenth component of the graded generalized local cohomology module. In this paper we study the asymptotic behavior of AssfR+() as n → –∞ wheneverkis the least integerjfor which the ordinary local cohomology moduleis not finitely generated.

scholarly journals Finiteness properties of generalized local cohomology modules for minimax modules

2017 ◽  
Vol 4 (1) ◽  
pp. 1327683
Author(s):  
Sh. Payrovi ◽  
I. Khalili-Gorji ◽  
Z. Rahimi-Molaei ◽  
Lishan Liu
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Minimax Modules ◽  
Generalized Local Cohomology Modules ◽  
Finiteness Properties ◽  
Cohomology Modules

ON THE FINITENESS PROPERTIES OF THE GENERALIZED LOCAL COHOMOLOGY MODULES

2002 ◽  
Vol 30 (2) ◽  
pp. 859-867 ◽  
Author(s):  
J. Asadollahi ◽  
K. Khashyarmanesh ◽  
Sh. Salarian
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Finiteness Properties ◽  
Cohomology Modules

Ideal transforms and local cohomology defined by a pair of ideals

2018 ◽  
Vol 17 (10) ◽  
pp. 1850200
Author(s):  
L. Z. Chu ◽  
V. H. Jorge Pérez ◽  
P. H. Lima
Keyword(s):  
Algebraic Structure ◽  
Local Cohomology ◽  
Associated Primes ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules ◽  
The Ideal

In this paper, we introduce a generalization of the ordinary ideal transform, denoted by [Formula: see text], which is called the ideal transform with respect to a pair of ideals [Formula: see text] and has an apparent algebraic structure. Then we study its various properties and explore the connection with the ordinary ideal transform. Also, we discuss the associated primes of local cohomology modules with respect to a pair of ideals. In particular, we give a characterization for the associated primes of the nonvanishing generalized local cohomology modules.

Finiteness Results on Generalized Local Cohomology Modules

2009 ◽  
Vol 16 (01) ◽  
pp. 65-70
Author(s):  
Naser Zamani
Keyword(s):  
Local Ring ◽  
Local Cohomology ◽  
Associated Primes ◽  
Finitely Generated ◽  
Local Cohomology Module ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules

Let (R, 𝔪) be a local ring, 𝔞 an ideal of R, and M, N be two finitely generated R-modules. We show that r = gdepth (M/𝔞M, N) is the least integer such that [Formula: see text] has infinite support. Also, we prove that the first non-Artinian generalized local cohomology module has finitely many associated primes.

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.

FINITENESS PROPERTIES OF LOCAL COHOMOLOGY MODULES AND GENERALIZED REGULAR SEQUENCES

2010 ◽  
Vol 09 (02) ◽  
pp. 315-325
Author(s):  
KAMAL BAHMANPOUR ◽  
SEADAT OLLAH FARAMARZI ◽  
REZA NAGHIPOUR
Keyword(s):  
Nonnegative Integer ◽  
Local Cohomology ◽  
Regular Sequence ◽  
Associated Primes ◽  
Finitely Generated ◽  
Commutative Noetherian Ring ◽  
Regular Sequences ◽  
Local Cohomology Modules ◽  
Finiteness Properties ◽  
Cohomology Modules

Let R be a commutative Noetherian ring, 𝔞 an ideal of R, and M an R-module. The purpose of this paper is to show that if M is finitely generated and dim M/𝔞M > 1, then the R-module ∪{N|N is a submodule of [Formula: see text] and dim N ≤ 1} is 𝔞-cominimax and for some x ∈ R is Rx + 𝔞-cofinite, where t ≔ gdepth (𝔞, M). For any nonnegative integer l, it is also shown that if R is semi-local and M is weakly Laskerian, then for any submodule N of [Formula: see text] with dim N ≤ 1 the associated primes of [Formula: see text] are finite, whenever [Formula: see text] for all i < l. Finally, we show that if (R, 𝔪) is local, M is finitely generated, [Formula: see text] for all i < l, and [Formula: see text] then there exists a generalized regular sequence x1, …, xl ∈ 𝔞 on M such that [Formula: see text].

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