Results 131 to 140 of about 6,938,375 (155)

Modules of generalized fractions and general local cohomology modules

Archiv der Mathematik, 1987
Let A be a commutative Noetherian ring with identity. Following the author [J. Lond. Math. Soc., II. Ser. 19, 402-410 (1979; Zbl 0396.13016)] a non-empty set of ideals of A, say \(\Phi\), is called a system of ideals of whenever \({\mathfrak a},{\mathfrak b}\in \Phi\), then there is an ideal \({\mathfrak c}\) in \(\Phi\) such that \({\mathfrak c ...
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Associated primes of local cohomology modules of generalized Laskerian modules

Czechoslovak Mathematical Journal, 2019
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Hassanzadeh-Lelekaami, Dawood, Roshan-Shekalgourabi, Hajar   +1 more
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Cofiniteness of generalized local cohomology modules

Journal of Algebra and Its Applications
Let [Formula: see text] be an ideal of a commutative noetherian ring [Formula: see text] and [Formula: see text] two [Formula: see text]-modules with [Formula: see text] finitely generated. It is shown that if either [Formula: see text] is an [Formula: see text]-cofinite module of dimension [Formula: see text] for all [Formula: see text], or [Formula ...
Jingwen Shen, Xiaoyan Yang
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Generalized Regular Sequence and Finiteness of Local Cohomology Modules

Algebra Colloquium, 2008
Let R be a commutative Noetherian local ring, 𝔞 an ideal of R, and M a finitely generated generalized f-module. Let t be a positive integer such that [Formula: see text] and t > dim M - dim M/𝔞M. In this paper, we prove that there exists an ideal 𝔟 ⊇ 𝔞 such that (1) dim M - dim M/𝔟M = t; and (2) the natural homomorphism [Formula: see text] is an ...
Mafi, A., Saremi, H.
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Local Cohomology and Maximal Generalized Modules

Asian Journal of Mathematics and Computer Research
Aims: Study of commutative algebra.Study Design: Cross-sectional study.Place and Duration of Study: University of São Paulo, August 2021 to October 2022.Methodology: Study through books and articles.Results: The article study the relation between local cohomology defined by an ideal and cohomological dimension.Conclusion: With the results of the paper,
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Non-vanishing and cofiniteness of generalized local cohomology modules

Periodica Mathematica Hungarica
The ambient category is that of finitely generated modules over commutative Noetherian ring \(R\). \(M\) denotes a finitely generated \(R\)-module and \(I\) an ideal of \(R\), and in particular for dim\(R/I\leq 1\). For another \(R\)-module \(N\) and an integer \(i\geq 0\), the \(i\)th generalized local cohomology module of the pair \(M, N\), with ...
Tran Tuan Nam, Nguyen Minh Tri
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ON THE NON-VANISHING AND THE ARTINIANNESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Journal of Algebra and Its Applications, 2013
We study top generalized local cohomology modules and get important properties about the vanishing, non-vanishing and the artinianness of generalized local cohomology modules.
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On the Artinian Property of Certain General Local Cohomology Modules

Journal of the London Mathematical Society, 1985
Let A be a commutative Noetherian local ring with Krull dimension n. \textit{R. Y. Sharp} [Proc. Edinb. Math. Soc., II. Ser. 24, 9-14 (1981; Zbl 0483.13007)] has proved that \(H^ n_ a(A)\), the n-th local cohomology module of A with respect to the ideal a, is an Artinian A-module.
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General local cohomology modules and Faltings' local-global principles

Summary: In this article, we study the local-global principles for the Artinianness of ordinary local cohomology modules and the finiteness of general local cohomology modules. Let \(R\) be a Noetherian ring, \(\Phi\) be a system of ideals of \(R\) and \(N\) be an \(R\)-module. Assume that \(\mathcal{S}\) is a Serre subcategory of Mod\((R)\) satisfying
Sadeghi, MirYousef, Amoli, Khadijeh Ahmadi, Fazel, Reza Arian   +2 more
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Co-Cohen-Macaulay Modules and Generalized Local Cohomology

Algebra Colloquium, 2011
Let (R,𝔪) be a Noetherian local ring, 𝔞 a proper ideal of R, and M, N two finitely generated R-modules of finite projective dimension m and of finite dimension n, respectively. It is shown that if n ≤ 2, then the generalized local cohomology module [Formula: see text] is a co-Cohen-Macaulay module.
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