On the finiteness properties of extension and torsion functors of local cohomology modules

Khashyarmanesh, Kazem

doi:10.1090/s0002-9939-06-08664-3

Cited by 29 publications

(12 citation statements)

References 17 publications

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“…The part i follows from Theorem 2.10 and the fact that the Bass numbers of finitely generated modules are finite. Also, ii follows from Theorem 2.10 and [11,Corollary 3.5].…”

Section: M/s M/t / S/t = N/kmentioning

confidence: 97%

Faltings’ Local-global Principle for the Finiteness of Local Cohomology Modules over Noetherian Rings

Mehrvarz

Naghipour

Sedghi

2015

Communications in Algebra

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Let R denote a commutative Noetherian (not necessarily local) ring, an ideal of R and M a finitely generated R-module. The purpose of this article is to show that f n M = inf 0 ≤ i ∈ dim H i M /N ≥ n for any finitely generated submodule N ⊆ H i M , where n is a non-negative integer and the invariant f n M = inf f R M ∈ SuppM/ M and dim R/ ≥ n is the nth finiteness dimension of M relative to . As a consequence, it follows that the set Ass R ⊕ f n M i=0 H i M ∩ ∈ SpecR dim R/ ≥ n is finite. This generalizes the main result of Quy [10], Brodmann and Lashgari [5], and Asadollahi and Naghipour [1].

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“…The part i follows from Theorem 2.10 and the fact that the Bass numbers of finitely generated modules are finite. Also, ii follows from Theorem 2.10 and [11,Corollary 3.5].…”

Section: M/s M/t / S/t = N/kmentioning

confidence: 97%

Faltings’ Local-global Principle for the Finiteness of Local Cohomology Modules over Noetherian Rings

Mehrvarz

Naghipour

Sedghi

2015

Communications in Algebra

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“…Huneke and Sharp [9] (in the case of positive characteristic) and Lyubeznik [17] (in characteristic zero) have shown that if R is regular local ring containing a field, then H n a ðRÞ has only finitely many associated primes for all n A N. Afterward, Lyubeznik [18] has prove this result also holds for any unramified regular local ring of mixed characteristic. We refer the reader to the papers of [21], [14], [22], [28] and [12]. There are several papers devoted to the extension of the above results.…”

Section: Introductionmentioning

confidence: 96%

On the finiteness properties of associated primes of generalized local cohomology modules

Khashyarmanesh

2008

Forum Mathematicum

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Let R be a commutative Noetherian ring, a an ideal of R and N an R-module. We prove that, for every finitely generated R-module of finite projective dimension t, the elements in the support of generalized local cohomology module H nþt a ðM; NÞ of height n are finite for all n b 0. This implies that, if R is a d-dimensional local ring, then H dþtÀ1 a ðM; NÞ has finite support for arbitrary R, a and N. In addition, for a non-negative integer n, we show that if M and N are arbitrary finitely generated R-modules such that the R-modules H i a ðNÞ and H i a ðM; NÞ have finite support for all i < n, then Ass H n a ðM; NÞ is finite.

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“…This result inspired us to study Tor R i (R/a, H j a (X)) in general for an arbitrary R-module X. Note that there are some attempts to study Tor R 0 (R/a, H j a (X)) in [2] and Tor R i (R/a, H j a (M )) in [10].…”

Section: Introductionmentioning

confidence: 98%

Torsion Functors of Local Cohomology Modules

Aghapournahr¹,

Taherizadeh

Vahidi

2009

Algebr Represent Theor

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On the finiteness properties of extension and torsion functors of local cohomology modules

Abstract: Abstract. Let R be a commutative Noetherian ring with non-zero identity, a and b ideals of R with a ⊆ b,

Cited by 29 publications

References 17 publications

Faltings’ Local-global Principle for the Finiteness of Local Cohomology Modules over Noetherian Rings

Faltings’ Local-global Principle for the Finiteness of Local Cohomology Modules over Noetherian Rings

On the finiteness properties of associated primes of generalized local cohomology modules

Torsion Functors of Local Cohomology Modules

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