Hilbert-Kirby Polynomials in Generalized Local Cohomology Modules

2021 ◽  
Author(s):  
M. Shafiei ◽  
A. Khojali ◽  
A. Azari ◽  
N. Zamani
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
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.

On ideals preserving generalized local cohomology modules

2015 ◽  
Vol 15 (01) ◽  
pp. 1650019 ◽  
Author(s):  
Tsutomu Nakamura
Keyword(s):  
Positive Integer ◽  
Noetherian Ring ◽  
Local Cohomology ◽  
Finitely Generated ◽  
Commutative Noetherian Ring ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules ◽  
The Ideal

Let R be a commutative Noetherian ring, 𝔞 an ideal of R and M, N two finitely generated R-modules. Let t be a positive integer or ∞. We denote by Ωt the set of ideals 𝔠 such that [Formula: see text] for all i < t. First, we show that there exists the ideal 𝔟t which is the largest in Ωt and [Formula: see text]. Next, we prove that if 𝔡 is an ideal such that 𝔞 ⊆ 𝔡 ⊆ 𝔟t, then [Formula: see text] for all i < t.

Some homological properties of generalized local cohomology modules

2019 ◽  
Vol 18 (12) ◽  
pp. 1950238
Author(s):  
Yavar Irani ◽  
Kamal Bahmanpour ◽  
Ghader Ghasemi
Keyword(s):  
Local Ring ◽  
Local Cohomology ◽  
Finitely Generated ◽  
Noetherian Local Ring ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules

Let [Formula: see text] be a Noetherian local ring and [Formula: see text], [Formula: see text] be two finitely generated [Formula: see text]-modules. In this paper, it is shown that [Formula: see text] and [Formula: see text] for each [Formula: see text] and each integer [Formula: see text]. In particular, if [Formula: see text] then [Formula: see text]. Moreover, some applications of these results will be included.

Cohomological Dimension of Generalized Local Cohomology Modules

2008 ◽  
Vol 15 (02) ◽  
pp. 303-308 ◽  
Author(s):  
Jafar Amjadi ◽  
Reza Naghipour
Keyword(s):  
Exact Sequence ◽  
Noetherian Ring ◽  
Local Cohomology ◽  
Cohomological Dimension ◽  
Algebraic Varieties ◽  
Finitely Generated ◽  
Commutative Noetherian Ring ◽  
Local Cohomology Modules ◽  
Generalized Local Cohomology Modules ◽  
Cohomology Modules

The study of the cohomological dimension of algebraic varieties has produced some interesting results and problems in local algebra. Let 𝔞 be an ideal of a commutative Noetherian ring R. For finitely generated R-modules M and N, the concept of cohomological dimension cd 𝔞(M, N) of M and N with respect to 𝔞 is introduced. If 0 → N' → N → N'' → 0 is an exact sequence of finitely generated R-modules, then it is shown that cd 𝔞(M, N) = max { cd 𝔞(M, N'), cd 𝔞(M, N'')} whenever proj dim M < ∞. Also, if L is a finitely generated R-module with Supp (N/Γ𝔞(N)) ⊆ Supp (L/Γ𝔞(L)), then it is proved that cd 𝔞(M, N) ≤ max { cd 𝔞(M,L), proj dim M}. Finally, as a consequence, a result of Brodmann is improved.

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