A Finiteness Result for Associated Primes of Certain Ext-Modules

Brodmann, Markus; Nhan, Le Thanh

doi:10.1080/00927870701869543

Cited by 22 publications

(12 citation statements)

References 8 publications

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“…Most of the properties are familiar results for the cases k = −1, k = 0, and k = 1, cf. [5], [10], [1], and [3]. In the local case, it is shown, ( [8], Lemma 3.4), that the local cohomology with respect to the maximal ideal of R is concerned with the local cohomology with respect to an ideal generated by any filter regular sequence.…”

Section: Introductionmentioning

confidence: 99%

On THE Κ-Regular SEQUENCES AND THE GENERALIZATION OF F-Modules

Ahmadi-Amoli¹,

Sanaei²

2012

Journal of the Korean Mathematical Society

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Abstract. For a given ideal I of a Noetherian ring R and an arbitrary integer k ≥ −1, we apply the concept of k-regular sequences and the notion of k-depth to give some results on modules called k-Cohen Macaulay modules, which in local case, is exactly the k-modules (as a generalization of f-modules). Meanwhile, we give an expression of local cohomology with respect to any k-regular sequence in I, in a particular case. We prove that the dimension of homology modules of the Koszul complex with respect to any k-regular sequence is at most k. Therefore homology modules of the Koszul complex with respect to any filter regular sequence has finite length.

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Section: Introductionmentioning

confidence: 99%

On THE Κ-Regular SEQUENCES AND THE GENERALIZATION OF F-Modules

Ahmadi-Amoli¹,

Sanaei²

2012

Journal of the Korean Mathematical Society

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“…, x nr r )R) to be finite. Nhan and Hoang [9] introduced the notion of A-cosequence in dimension > k, which is in some sense dual to the notion of M -sequence in dimension > k was introduced by Brodmann and Nhan in [2]. Following Nhan and Hoang [9], a sequence (x 1 , .…”

Section: Introductionmentioning

confidence: 99%

THE STABILITY OF CERTAIN SETS OF ATTACHED PRIME IDEALS RELATED TO COSEQUENCE IN DIMENSION > k

Khanh¹

2016

Bulletin of the Korean Mathematical Society

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Abstract. Let (R, m) be a Noetherian local ring, I, J two ideals of R, and A an Artinian R-module. Let k ≥ 0 be an integer and r = Width >k (I, A) the supremum of lengths of A-cosequences in dimension > k in I defined by . It is first shown that for each t ≤ r and each sequence x 1 , . . . , xt which is an A-cosequence in dimension > k, the setis independent of the choice of n 1 , . . . , nt. Let r be the eventual value of Width >k (0 : A J n ). Then our second result says that for each t ≤ r the set (Att R (Tor R i (R/I, (0 : A J n )))) ≥k is stable for large n.

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“…Next, by using the notion of M-sequences in dimension > k, Brodmann and Nhan [3] proved that, for an integer…”

Section: Introductionmentioning

confidence: 99%

On Finiteness Properties on Associated Primes of Local Cohomology Modules and Ext-Modules

Chu¹,

Wang²

2014

Journal of the Korean Mathematical Society

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Abstract. Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a finitely generated R-module. In this paper, by computing the local cohomology modules and Ext-modules via the injective resolution of M , we proved that, if for an integer t > 0,for ∀ j ≤ t and ∀ n > 0. This shows that n>0 (Ass R Ext i R (R/I n , M )) ≥k is a finite set for ∀ i ≤ t. Also, we prove that

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A Finiteness Result for Associated Primes of Certain Ext-Modules

Abstract: Abstract1 . Using some properties of unconditioned M −sequences in dimension > s, we give a finiteness result for the set

Cited by 22 publications

References 8 publications

On THE Κ-Regular SEQUENCES AND THE GENERALIZATION OF F-Modules

On THE Κ-Regular SEQUENCES AND THE GENERALIZATION OF F-Modules

THE STABILITY OF CERTAIN SETS OF ATTACHED PRIME IDEALS RELATED TO COSEQUENCE IN DIMENSION > k

On Finiteness Properties on Associated Primes of Local Cohomology Modules and Ext-Modules

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