Cominimaxness of local cohomology modules

Aghapournahr, Moharram

doi:10.21136/cmj.2018.0161-17

Cited by 4 publications

(6 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We are now ready to state and prove the first main theorem of this section. The following theorem is a generalization of [4,11,Proposition 2.6] and [3,27,Proposition 2.4]. In fact, we remove I-torsion condition from these propositions.…”

Section: Et H-cominimax Modules With Respect To An Idealmentioning

confidence: 99%

“…the class of I-cofinite FD ≤1 modules), for all ideals I in a commutative Noetherian ring R. Also in [27] (resp. [3]) it is proved that the same question is true for the category of all I-cominimax R-modules M with dim M ≤ 1 (resp. the class of I-cominimax FD ≤1 modules), for all ideals I in R. In this direction we introduced the concept of I-ET H-cominimax or ET H-cominimax modules with respect to I in Definition 2.1.…”

Section: Introductionmentioning

confidence: 95%

“…The general local cohomology module H j Φ (M ) is defined to be Φ-cominimax if there exists an ideal I ∈ Φ such that Ext i R (R/I, H j Φ (M )) is minimax, for all i, j ≥ 0. Recently many authors studied the minimaxness and cominimaxness of local cohomology modules and answered the Conjecture 1.1 and Question 1.2 in the class of minimax modules in some cases (see [1,3,9,14,24,27,29]). The purpose of this note is to make a suitable generalization of Conjecture 1.1 and Question 1.2 in terms of minimax modules instead of finitely generated modules for general local cohomology modules.…”

Section: Introductionmentioning

confidence: 99%

“…it is shown that Hartshorne's question is true for the category of all I-cofinite R-modules M with dim M ≤ 1 (resp. the class of I-cofinite FD ≤1 modules), for all ideals I in a commutative Noetherian ring R. Also in[27] (resp [3]…”

mentioning

confidence: 99%

“…Proposition 2.6] and[3,27, Proposition 2.4]. In fact, we remove I-torsion condition from these propositions.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Cominimaxness of certain general local cohomology modules

Aghapournahr¹

2019

HJMS

Self Cite

View full text Add to dashboard Cite

Let R be a commutative Noetherian ring, Φ a system of ideals of R and I ∈ Φ. Let t ∈ N 0 be an integer and M an R-module such that Ext i R (R/I, M) is minimax for all i ≤ t+1. We prove that if the R-module H i Φ (M) is FD ≤1 (or weakly Laskerian) for all i < t, then H i Φ (M) is Φ-cominimax for all i < t and for any FD ≤0 (or minimax) submodule N of H t Φ (M), the R-modules Hom R (R/I, H t Φ (M)/N) and Ext 1 R (R/I, H t Φ (M)/N) are minimax. Let N be a finitely generated R-module. We also prove that Ext j R (N, H i Φ (M)) and Tor R j (N, H i Φ (M)) are Φ-cominimax for all i and j whenever M is minimax and H i Φ (M) is FD ≤1 (or weakly Laskerian) for all i.

show abstract

Section: Et H-cominimax Modules With Respect To An Idealmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

“…Proposition 2.6] and[3,27, Proposition 2.4]. In fact, we remove I-torsion condition from these propositions.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Cominimaxness of certain general local cohomology modules

Aghapournahr¹

2019

HJMS

Self Cite

View full text Add to dashboard Cite

show abstract

Finiteness properties of extension functors of cominimax modules

Karimirad

Aghapournahr

Bahmanpour

2021

Communications in Algebra

View full text Add to dashboard Cite

Cominimaxness with respect to ideals of dimension two and local cohomology

Karimirad

Aghapournahr

2020

J. Algebra Appl.

View full text Add to dashboard Cite

Let [Formula: see text] be a commutative Noetherian ring, [Formula: see text] an ideal of [Formula: see text] and [Formula: see text] an [Formula: see text]-module with [Formula: see text]. We get equivalent conditions for top local cohomology module [Formula: see text] to be Artinian and [Formula: see text]-cofinite Artinian separately. In addition, we prove that if [Formula: see text] is a local ring such that [Formula: see text] is minimax, for each [Formula: see text], then [Formula: see text] is minimax [Formula: see text]-module for each [Formula: see text] and for each finitely generated [Formula: see text]-module [Formula: see text] with [Formula: see text] and [Formula: see text]. As a consequence we prove that if [Formula: see text] and [Formula: see text], then [Formula: see text] is [Formula: see text]-cominimax if (and only if) [Formula: see text], [Formula: see text] and [Formula: see text] are minimax. We also prove that if [Formula: see text] and [Formula: see text] such that [Formula: see text] is minimax for all [Formula: see text], then [Formula: see text] is [Formula: see text]-cominimax for all [Formula: see text] if (and only if) [Formula: see text] is minimax for all [Formula: see text].

show abstract

Cominimaxness of local cohomology modules

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Cited by 4 publications

References 34 publications

Cominimaxness of certain general local cohomology modules

Cominimaxness of certain general local cohomology modules

Finiteness properties of extension functors of cominimax modules

Cominimaxness with respect to ideals of dimension two and local cohomology

Contact Info

Product

Resources

About