Results 71 to 80 of about 104 (95)

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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Duality and vanishing of generalized local cohomology

Archiv der Mathematik, 2003
Let \((R, \mathfrak m)\) be a local Noetherian ring, and let \(M, N\) be two \(R\)-modules. \textit{J. Herzog} [``Komplexe, Auflösungen und Dualität in der lokalen Algebra'', Habilitationsschrift (Univ. Regensburg 1970)], the first author introduced the notion of \(H^i_{\mathfrak m}(M,N) = \varinjlim \text{ Ext}^i_R(M/\mathfrak m^n M,N),\) the ...
Herzog, Jürgen, Zamani, Naser
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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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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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Artinian graded generalized local cohomology

Journal of Algebra and Its Applications, 2015
Let R = ⨁j≥0 Rj be a homogeneous Noetherian ring with irrelevant ideal R+ = ⨁j≥1 Rj. Let M, N be two finitely generated graded R-modules. Several results on the Artinianness, tameness and asymptotic property of the graded R-modules [Formula: see text] will be investigated.
Zamani, Naser, Khojali, Ahmad
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Generalized local cohomology and Serre cohomological dimension

Summary: Let \(R\) be a commutative Noetherian ring, \(I \), \(J\) be two ideals of \(R\), and \(M\), \(N\) be two \(R\)-modules. Let \(S\) be a Serre subcategory of the category of \(R\)-modules. We introduce Serre cohomological dimension of \(N\), \(M\) with respect to \((I, J)\), as \(\mathrm{cd}_S(I, J, N, M) = \sup\{i\in\mathbb{N}_0: H_{I, J}^i(N,
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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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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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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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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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