Results 61 to 70 of about 101 (88)

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 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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Attached Primes of the Top Generalized Local Cohomology Modules [PDF]

Bulletin of the Australian Mathematical Society, 2009
AbstractLet (R,𝔪) be a commutative Noetherian local ring, letIbe an ideal ofRand letMandNbe finitely generatedR-modules. Assume that$\mathrm {pd} (M)=d\lt \infty $,$\dim N=n\lt \infty $. First, we give the formula for the attached primes of the top generalized local cohomology moduleHId+n(M,N); later, we prove that if Att(HId+n(M,N))=Att(HJd+n(M,N ...
Gu, Yan, Chu, Lizhong
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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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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.
Tran Tuan Nam
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Associated primes of local cohomology modules of generalized Laskerian modules

Czechoslovak Mathematical Journal, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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Cominimaxness of generalized local cohomology modules

Bulletin of the Belgian Mathematical Society - Simon Stevin
This paper investigates the finiteness properties of generalized local cohomology modules. Let \(R\) be a commutative Noetherian ring with identity, and \(\mathfrak{a}\) an ideal of \(R\). For two \(R\)-modules \(X\) and \(Y,\) and an integer \(i\geq 0\), the \(i\)th \textit{generalized local cohomology} module of \(X\) and \(Y\) with respect to ...
Roshan-Shekalgourabi, Hajar, Hassanzadeh-Lelekaami, Dawood   +1 more
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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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