Results 121 to 130 of about 6,938,375 (155)

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
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A note on graded generalized local cohomology modules

Quaestiones Mathematicae, 2017
Let R = ⊕n∈N0Rn be a positively graded commutative Noetherian ring with irrelevant ideal R+ = ⊕n∈NRn and let a be a graded ideal contained in R+. Let M, N be two finitely generated graded R-modules. In this paper, we study the finiteness and vanishing of
Saremi, Hero
exaly   +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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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 the generalized local cohomology of minimax modules

Journal of Algebra and Its Applications, 2016
Let [Formula: see text] be a commutative Noetherian ring with identity and [Formula: see text] be an ideal of [Formula: see text]. Assume that [Formula: see text] is a finite [Formula: see text]-module and [Formula: see text] and [Formula: see text] are minimax [Formula: see text]-modules such that [Formula: see text].
Roshan-Shekalgourabi, H., Hassanzadeh-Lelekaami, D.   +1 more
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Hilbert-Kirby Polynomials in Generalized Local Cohomology Modules

Acta Mathematica Vietnamica, 2021
Let \((R_0,{\mathfrak m}_0,k_0)\) be a local ring and \(R=R_0[R_1]\) a commutative Noetherian graded ring. Let \(M\) and \(N\) be two \(\mathbb{Z}\)-graded finitely generated \(R\)-modules and \(R_+\) denote the irrelevant ideal of \(R\). The paper under review studies the asymptotic behaviour of the graded pieces of the graded generalized local ...
Shafiei, M., Khojali, A., Azari, A., Zamani, N.   +3 more
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Finiteness Results on Generalized Local Cohomology Modules

Algebra Colloquium, 2009
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.
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On the Finiteness Results of the Generalized Local Cohomology Modules

Algebra Colloquium, 2009
Let 𝔞 be an ideal of a commutative Noetherian local ring R, and let M and N be two finitely generated R-modules. Let t be a positive integer. It is shown that if the support of the generalized local cohomology module [Formula: see text] is finite for all i < t, then the set of associated prime ideals of the generalized local cohomology module ...
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Local cohomology and modules of generalized fractions

Mathematika, 1982
The purpose of this paper is to provide additional evidence to support our view that the modules of generalized fractions introduced in [8] are worth further investigation: we show that, for a module M over a (commutative, Noetherian) local ring A (with identity) having maximal ideal m and dimension n, the n-th local cohomology module may be viewed as ...
Sharp, R. Y., Zakeri, H.
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