Results 61 to 70 of about 104 (95)

On the Artinianness of Generalized Local Cohomology

Communications in Algebra, 2007
Let R be a commutative Noetherian local ring, I a proper ideal of R, M, and N finitely generated R-modules. It is proved that f-depth(I + Ann(M), N) is the least integer r such that the generalized local cohomology module is not Artinian. Let r ≥ 0 be an integer. We also discuss the property that is Artinian for all i ≥ r.
Zhongming Tang
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Results on Graded Generalized Local Cohomology

Communications in Algebra, 2008
Let R = ⨁ i≥0 R i be a positively graded Noetherian ring with irrelevant ideal R + = ⨁ i≥1 R i , and let M, N be two finitely generated graded R-modules such that pd(M) is finite. We show that the least integer i for which is not asymptotically zero is equal to the least integer i such that . Also, whenever R is homogeneous with local base ring (R 0, &#
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General Local Cohomology Modules with Small Dimensions

Vietnam Journal of Mathematics, 2022
Let \(R\) be a commutative Noetherian ring, \(\Phi\) a system of ideals of \(R\), \(M\) a finitely generated \(R\)-module, and \(n\) an integer. n this article, the authors introduce the notion \(n\)-\(\operatorname{depth}(\Phi, M)= \inf\{n\)-\(\operatorname{depth}(\mathfrak{a}, M): \mathfrak{a}\in \Phi\}\) and show that if \(-1\leq n\leq 1\), then \(n\
Nguyen Minh Tri, Bui Thi Hong Cam
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Cohomological Dimension of Generalized Local Cohomology Modules

Algebra Colloquium, 2008
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.
Amjadi, Jafar, Naghipour, Reza
openaire   +1 more source

A Note on the Artinianness and Vanishing of Local Cohomology and Generalized Local Cohomology Modules

Algebra Colloquium, 2009
The first part of this paper is concerned with the Artinianness of certain local cohomology modules [Formula: see text] when M is a Matlis reflexive module over a commutative Noetherian complete local ring R and 𝔞 is an ideal of R. Also, we characterize the set of attached prime ideals of [Formula: see text], where n is the dimension of M.
Khashyarmanesh, K., Khosh-Ahang, F.
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COFINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Bulletin of the Australian Mathematical Society, 2011
AbstractLet 𝔞 be an ideal of a Noetherian ring R. Let s be a nonnegative integer and let M and N be two R-modules such that ExtjR(M/𝔞M,Hi𝔞(N)) is finite for all i<s and all j≥0 . We show that HomR (R/𝔞,Hs𝔞(M,N)) is finite provided ExtsR(M/𝔞M,N) is a finite R-module.
Borna, Keivan, Sahandi, Parviz, Yassemi, Siamak   +2 more
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On the Finiteness Property of Generalized Local Cohomology Modules

Algebra Colloquium, 2005
Let [Formula: see text] be an ideal of a commutative Noetherian ring R, and let M and N be finitely generated R-modules. Let [Formula: see text] be the [Formula: see text]-finiteness dimension of N. In this paper, among other things, we show that for each [Formula: see text], (i) the set of associated prime ideals of generalized local cohomology ...
Khashyarmanesh, K., Yassi, M.
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On graded generalized local cohomology

Archiv der Mathematik, 2006
Let \( R = {\mathop \oplus \limits_{i\underline{\underline > } 0} }R_{i} \) be a homogeneous Noetherian ring with local base ring (R0,m0) and let M,N be two finitely generated graded R-modules. Let \( H^{i}_{{R + }} {\left( {M,N} \right)} \) denote the i-th graded generalized local cohomology of N relative to M with support in \( R = {\mathop \oplus ...
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Local cohomology and cohomology of certain generalized hughes complexes

Communications in Algebra, 1998
The main purpose of this paper is to show that cohomology modules of generalized Hughes complexes with respect to certain special systems of ideals are isomorphic to (generalized) local cohomology modules.
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Local cohomology, d-sequences and generalized fractions

Colloquium Mathematicum, 1998
Local cohomology modules are calculated by using Čech complexes. \textit{H. Zakeri} defined another complex by using the generalized fraction module, which was introduced by \textit{R. Y. Sharp} and \textit{H. Zakeri}, instead of usual fraction modules and uses it to calculate local cohomology with respect to the ideal generated by a \(d\)-sequence. In
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