Asymptotic behaviour of certain sets of associated prime ideals of Ext-modules

Khashyarmanesh, Kazem; Khosh-Ahang, Fahimeh

doi:10.1007/s00229-007-0152-9

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K Khashyarmanesh and F Khosh-ahang1

Lemma 22 Let S T Be Two Non-negative Integers Such That1

Introduction1

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Cited by 5 publications

(3 citation statements)

References 14 publications

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“…The following result, which is a nice consequence of Corollary 4.2, is a generalization of Theorem 2.9(i) in [15].…”

Section: K Khashyarmanesh and F Khosh-ahangmentioning

confidence: 59%

See 1 more Smart Citation

On the Behavior of Applying Derived Functors of Torsion Functors on Local Cohomology Modules

Khashyarmanesh

Khosh-Ahang

2012

J. Algebra Appl.

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“…The following result, which is a nice consequence of Corollary 4.2, is a generalization of Theorem 2.9(i) in [15].…”

Section: K Khashyarmanesh and F Khosh-ahangmentioning

confidence: 59%

“…There are a lot of papers devoted to studying the properties of (generalized) local cohomology modules or derived functors of these modules (e.g. [1,5,10,14,15,22]). …”

Section: Introductionmentioning

confidence: 99%

On the Behavior of Applying Derived Functors of Torsion Functors on Local Cohomology Modules

Khashyarmanesh

Khosh-Ahang

2012

J. Algebra Appl.

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“…Since the set ( j≥0 Ass Ext i R (M/a j M, N )) >s is contained in (Supp (M/aM ) ∩ Supp(N )) >s for all i, without loss of generality, we may assume that dim(N/(a + Ann(M ))N ) > s. Now, by using [14,Lemma 2.4], the result follows. Lemma 2.6.…”

Section: Lemma 22 Let S T Be Two Non-negative Integers Such Thatmentioning

confidence: 81%

Finiteness Dimension and Bass Numbers of Generalized Local Cohomology Modules

Saremi

Mafi

2013

J. Algebra Appl.

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Let R be a commutative Noetherian ring, a an ideal of R, and M , N two nonzero finitely generated R-modules. Let t be a non-negative integer. It is shown that dim Supp H i a (M, N ) ≤ 1 for all i < t if and only if there exists an ideal b of R such that dim R/b ≤ 1 and H i a (M, N ) ∼ = H i b (M, N ) for all i < t. As a consequence all Bass numbers and all Betti numbers of generalized local cohomology modules H i a (M, N ) are finite for all i < t, provided that the projective dimension pd(M ) is finite.

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Local Cohomology Modules, Serre Subcategories and Derived Functors of Torsion Functors

Khashyarmanesh

Khosh-Ahang

2012

Algebra Colloq.

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In this research, by using filter regular sequences, we obtain some exact sequences of right or left derived functors of local cohomology modules. Then we use them to gain some conditions under which a right or left derived functor of some special functors over local cohomology modules belongs to a Serre subcategory. These results can conclude some generalizations of previous results in this context or regain some of them.

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Asymptotic behaviour of certain sets of associated prime ideals of Ext-modules

Cited by 5 publications

References 14 publications

On the Behavior of Applying Derived Functors of Torsion Functors on Local Cohomology Modules

On the Behavior of Applying Derived Functors of Torsion Functors on Local Cohomology Modules

Finiteness Dimension and Bass Numbers of Generalized Local Cohomology Modules

Local Cohomology Modules, Serre Subcategories and Derived Functors of Torsion Functors

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