Results 51 to 60 of about 101 (88)
On the Associated Primes of Generalized Local Cohomology Modules [PDF]
Communications in Algebra, 2006 7 pages, to appear in Communications in ...
Amir Mafi
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Cofiniteness of Generalized Local Cohomology Modules
Bulletin of the Australian Mathematical Society, 2011AbstractLet 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.
Siamak Yassemi +2 more
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On the Finiteness Results of the Generalized Local Cohomology Modules
Algebra Colloquium, 2009Let 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 ...
Amir Mafi
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General Local Cohomology Modules with Small Dimensions
Vietnam Journal of Mathematics, 2022Let \(R\) 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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Cofiniteness and Finiteness of Generalized Local Cohomology Modules [PDF]
Bulletin of the Australian Mathematical Society, 2009 AbstractLet I be an ideal of a commutative Noetherian local ring R, and M and N two finitely generated modules. Let t be a positive integer. We mainly prove that (i) if HIi(M,N) is Artinian for all i<t, then HIi(M,N) is I-cofinite for all i<t and Hom(R/I,HIt(M,N)) is finitely generated; (ii) if d=pd(M)<∞ and dim N=n<∞, then HId+n(M,N) is I ...
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Cohomological Dimension of Generalized Local Cohomology Modules
Algebra Colloquium, 2008The 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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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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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, 2005Let [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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Hilbert-Kirby Polynomials in Generalized Local Cohomology Modules
Acta Mathematica Vietnamica, 2021Let \((R_0,{\mathfrak m}_0,k_0)\) 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. +3 more
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Local cohomology and modules of generalized fractions
Mathematika, 1982The 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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