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Journal articles on the topic 'Annihilator of local cohomology module'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Hasanzad, Masoumeh, and Jafar A’zami. "A short note on annihilators of local cohomology modules." Journal of Algebra and Its Applications 19, no. 02 (2019): 2050026. http://dx.doi.org/10.1142/s0219498820500267.

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Let [Formula: see text] be a commutative Noetherian domain, [Formula: see text] a nonzero [Formula: see text]-module of finite injective dimension, and [Formula: see text] be a nonzero ideal of [Formula: see text]. In this paper, we prove that whenever [Formula: see text], then the annihilator of [Formula: see text] is zero. Also, we calculate the annihilator of [Formula: see text] for finitely generated [Formula: see text]-modules [Formula: see text] and [Formula: see text] with conditions [Formula: see text] and [Formula: see text]. Moreover, if [Formula: see text] is a regular Noetherian lo

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2

Raghavan, K. "Uniform annihilation of local cohomology and of Koszul homology." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 3 (1992): 487–94. http://dx.doi.org/10.1017/s0305004100071164.

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Let R be a ring (all rings considered here are commutative with identity and Noetherian), M a finitely generated R-module, and I an ideal of R. The jth local cohomology module of M with support in I is defined byIn this paper, we prove a uniform version of a theorem of Brodmann about annihilation of local cohomology modules. As a corollary of this, we deduce a generalization of a theorem of Hochster and Huneke about uniform annihilation of Koszul homology.

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3

An, Trần Nguyên. "ANNIHILATOR OF LOCAL COHOMOLOGY MODULES AND STRUCTURE OF RINGS." TNU Journal of Science and Technology 225, no. 13 (2020): 73–77. http://dx.doi.org/10.34238/tnu-jst.3194.

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Cho (R, m) là vành Noether địa phương, A là R-môđun Artin, và M là R-môđun hữu hạn sinh. Ta có Ann R(M/ p M) = p với mọi p ∈ Var(Ann R M). Do đó rất tự nhiên ta xét tính chất sau về linh hóa tử của môđun ArtinAnn R(0 : A p) = p for all p ∈ Var(Ann R A). (∗)Cho i ≥ 0 là số nguyên. Alexander Grothendieck đã chỉ ra rằng môđun đối đồng điều địa phương Hi m(M) là Artin. Tính chất (∗) của các môđun đối đồng điều địa phương liên hệ mật thiết với cấu trúc vành cơ sở. Trong bài báo này, chúng tôi chỉ ra với mỗi p ∈ Spec(R) mà Hmi (R/ p) thỏa mãn tính chất (*) với mọi i thì R/ p là catenary phổ dụng và

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4

Divaani-Aazar, Kamran, and Majid Rahro Zargar. "The derived category analogues of Faltings Local-global Principle and Annihilator Theorems." Journal of Algebra and Its Applications 18, no. 07 (2019): 1950140. http://dx.doi.org/10.1142/s0219498819501408.

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Let [Formula: see text] be a specialization closed subset of Spec R and X a homologically left-bounded complex with finitely generated homologies. We establish Faltings’ Local-global Principle and Annihilator Theorems for the local cohomology modules [Formula: see text] Our versions contain variations of results already known on these theorems.

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5

BAGHERIYEH, IRAJ, KAMAL BAHMANPOUR, and GHADER GHASEMI. ""COFINITENESS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES"." Mathematical Reports 25(75), no. 1 (2022): 133–51. http://dx.doi.org/10.59277/mrar.2023.25.75.1.133.

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"Let R be a Noetherian ring and I be an ideal of R. Let M be a finitely generated R-module with cd(I,M) = t ≥ 0 and assume that L is the largest submodule of M such that cd(I,L) < cd(I,M). It is shown that AnnR Ht I (M) = AnnRM/L in each of the following cases: (i) dimM/IM ≤ 1. (ii) dimR/I ≤ 1. (iii) The R-module Hi I (M) is Artinian for each i ≥ 2. (iv) The R-module Hi I (R) is Artinian for each i ≥ 2. (v) cd(I,M) ≤ 1. (vi) cd(I,R) ≤ 1. (vii) The Rmodule Ht I (M) is Artinian and I-cofinite. These assertions answer affirmatively a question raised by Atazadeh et al. in [2], in some special c

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6

Khojali, Ahmad. "On Buchsbaum type modules and the annihilator of certain local cohomology modules." Czechoslovak Mathematical Journal 67, no. 4 (2017): 1021–29. http://dx.doi.org/10.21136/cmj.2017.0313-16.

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7

AMANALAHZADEH, Mahnaz, Jafar A’ZAMI, and Kamal BAHMANPOUR. "Lynch’s conjecture and annihilators of local cohomology modules." Proceedings of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science 25, no. 3 (2024): 181–85. http://dx.doi.org/10.59277/pra-ser.a.25.3.03.

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Let $R$ be a commutative Noetherian ring and $I$ be an ideal of $R$ with $\cd(I,R)=t\geq 1$. In this paper, we consider the Lynch's conjecture and we obtain a partial answer for this conjecture. More precisely, we show that if $M$ is an $R$-module such that $0\neq H^t_I(M)$ is $I$-cofinite, then $\Ann_RH^t_I(R)\subseteq \p$ for some minimal prime ideal $\p$ of $R$.

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8

Bahmanpour, Kamal. "Annihilators of Local Cohomology Modules." Communications in Algebra 43, no. 6 (2015): 2509–15. http://dx.doi.org/10.1080/00927872.2014.900687.

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9

Karimi, S., and Sh Payrovi. "Attached primes and annihilators of top local cohomology modules defined by a pair of ideals." Algebra and Discrete Mathematics 29, no. 2 (2020): 211–20. http://dx.doi.org/10.12958/adm429.

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10

Khashyarmanesh, Kazem. "On the Annihilators of Local Cohomology Modules." Communications in Algebra 37, no. 5 (2009): 1787–92. http://dx.doi.org/10.1080/00927870802216412.

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11

Bahmanpour, Kamal, Jafar Aʼzami, and Ghader Ghasemi. "On the annihilators of local cohomology modules." Journal of Algebra 363 (August 2012): 8–13. http://dx.doi.org/10.1016/j.jalgebra.2012.03.026.

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12

Asadollahi, Javad, and Shokrollah Salarian. "On the annihilation of local cohomology modules." Journal of Mathematics of Kyoto University 46, no. 2 (2006): 357–65. http://dx.doi.org/10.1215/kjm/1250281781.

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13

Zohouri, Maryam Mast. "On the annihilation of local cohomology modules." International Mathematical Forum 12 (2017): 527–30. http://dx.doi.org/10.12988/imf.2017.7110.

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14

REZAEI, Shahram. "On the annihilators of formal local cohomology modules." Hokkaido Mathematical Journal 48, no. 1 (2019): 195–206. http://dx.doi.org/10.14492/hokmj/1550480649.

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15

Brodmann, M., Ch Rotthaus, and R. Y. Sharp. "On annihilators and associated primes of local cohomology modules." Journal of Pure and Applied Algebra 153, no. 3 (2000): 197–227. http://dx.doi.org/10.1016/s0022-4049(99)00104-8.

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16

Atazadeh, Ali, Monireh Sedghi, and Reza Naghipour. "Cohomological dimension filtration and annihilators of top local cohomology modules." Colloquium Mathematicum 139, no. 1 (2015): 25–35. http://dx.doi.org/10.4064/cm139-1-2.

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17

Yoshizawa, Takeshi. "Annihilators of local cohomology modules over a Cohen-Macaulay ring." Journal of Algebra 594 (March 2022): 597–613. http://dx.doi.org/10.1016/j.jalgebra.2021.12.011.

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18

Phạm, Hữu Khánh. "Một số kết quả ổn định cho mô-đun M/I^{n}M". Tạp chí Khoa học Đại học Tây Nguyên (Tay Nguyen Journal of Science) 16, № 55 (2022): 28–31. https://doi.org/10.5281/zenodo.7323851.

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Cho (<em>R, m</em>) là vành giao hoán Noether địa phương, M là R-môđun Cohen-Macaulay hữu hạn sinh và I là iđêan của vành R mà không chứa trong bất kỳ iđêan nguyên tố cực tiểu nào của M. Trước hết chúng tôi chứng minh rằng tồn tại số nguyên <em>t</em><sub>1</sub> sao cho \(depth_{R_{p}} \) <em>(M/I<sup>n</sup>M)</em> = \(depth_{R_{p}} \)<sub> </sub><em>(M/I<sup>t<sub>1</sub></sup>M)</em><sub>p</sub>, với mọi <em>n ≥ t<sub>1</sub></em><sub> </sub>và mọi<em> p&

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19

Khashyarmanesh, K., and Sh Salarian. "Uniform Annihilation of Local Cohomology Modules Over a Gorenstein Ring." Communications in Algebra 34, no. 5 (2006): 1625–30. http://dx.doi.org/10.1080/00927870500542549.

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20

Tang, Zhongming. "A new depth and the annihilation of local cohomology modules." Archiv der Mathematik 90, no. 3 (2008): 200–208. http://dx.doi.org/10.1007/s00013-007-2101-y.

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21

Fathi, Ali. "Some bounds for the annihilators of local cohomology and Ext modules." Czechoslovak Mathematical Journal 72, no. 1 (2021): 265–84. http://dx.doi.org/10.21136/cmj.2021.0456-20.

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22

BAHMANPOUR, KAMAL. "EXACTNESS OF IDEAL TRANSFORMS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES." Journal of the Korean Mathematical Society 52, no. 6 (2015): 1253–70. http://dx.doi.org/10.4134/jkms.2015.52.6.1253.

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23

Rastgoo, Fahimeh, and Alireza Nazari. "Some results on the cofiniteness and annihilators of local cohomology modules." Communications in Algebra 46, no. 7 (2018): 3164–73. http://dx.doi.org/10.1080/00927872.2017.1407419.

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24

Atazadeh, Ali, Monireh Sedghi, and Reza Naghipour. "On the annihilators and attached primes of top local cohomology modules." Archiv der Mathematik 102, no. 3 (2014): 225–36. http://dx.doi.org/10.1007/s00013-014-0629-1.

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25

Boix, Alberto F., and Majid Eghbali. "Annihilators of local cohomology modules and simplicity of rings of differential operators." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 59, no. 4 (2018): 665–84. http://dx.doi.org/10.1007/s13366-018-0396-4.

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26

Atazadeh, Ali, Monireh Sedghi, and Reza Naghipour. "Some results on the annihilators and attached primes of local cohomology modules." Archiv der Mathematik 109, no. 5 (2017): 415–27. http://dx.doi.org/10.1007/s00013-017-1081-9.

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27

FATHI, ALI. "LOCAL-GLOBAL PRINCIPLE FOR THE FINITENESS AND ARTINIANNESS OF GENERALISED LOCAL COHOMOLOGY MODULES." Bulletin of the Australian Mathematical Society 87, no. 3 (2012): 480–92. http://dx.doi.org/10.1017/s0004972712000640.

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AbstractLet $\mathcal S$ be a Serre subcategory of the category of $R$-modules, where $R$ is a commutative Noetherian ring. Let $\mathfrak a$ and $\mathfrak b$ be ideals of $R$ and let $M$ and $N$ be finite $R$-modules. We prove that if $N$ and $H^i_{\mathfrak a}(M,N)$ belong to $\mathcal S$ for all $i\lt n$ and if $n\leq \mathrm {f}$-$\mathrm {grad}({\mathfrak a},{\mathfrak b},N )$, then $\mathrm {Hom}_{R}(R/{\mathfrak b},H^n_{{\mathfrak a}}(M,N))\in \mathcal S$. We deduce that if either $H^i_{\mathfrak a}(M,N)$ is finite or $\mathrm {Supp}\,H^i_{\mathfrak a}(M,N)$ is finite for all $i\lt n$,

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28

Runde, Volker. "Automatic continuity and second order cohomology." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 2 (2000): 231–43. http://dx.doi.org/10.1017/s1446788700001968.

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AbstractMany Banach algebras A have the property that, although there are discontinuous homomorphisms from A into other Banach algebras, every homomorphism from A into another Banach algebra is automatically continuous on a dense subspace—preferably, a subalgebra—of A. Examples of such algebras are C*-algebras and the group algebras L1(G), where G is a locally compact, abelian group. In this paper, we prove analogous results for , where E is a Banach space, and . An important rôle is played by the second Hochschild cohomology group of and , respectively, with coefficients in the one-dimensiona

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29

Khashyarmanesh, K., and F. Khosh-Ahang. "On The Annihilators of Derived Functors of Local Cohomology Modules and Finiteness Dimension." Communications in Algebra 41, no. 1 (2013): 215–25. http://dx.doi.org/10.1080/00927872.2011.629264.

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30

Tran, Nam Tuan, Tu Hoang Huy Nguyen, and Tri Minh Nguyen. "Top formal local cohomology module." Periodica Mathematica Hungarica 79, no. 1 (2018): 1–11. http://dx.doi.org/10.1007/s10998-018-0256-x.

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31

Khashyarmanesh, K., and Sh Salarian. "Faltings' theorem for the annihilation of local cohomology modules over a Gorenstein ring." Proceedings of the American Mathematical Society 132, no. 08 (2004): 2215. http://dx.doi.org/10.1090/s0002-9939-04-07322-8.

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32

Boix, Alberto F., and Majid Eghbali. "Correction to: Annihilators of local cohomology modules and simplicity of rings of differential operators." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 59, no. 4 (2018): 685–88. http://dx.doi.org/10.1007/s13366-018-0400-z.

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33

Lorestani, Keivan Borna, Parviz Sahandi, and Siamak Yassemi. "Artinian Local Cohomology Modules." Canadian Mathematical Bulletin 50, no. 4 (2007): 598–602. http://dx.doi.org/10.4153/cmb-2007-058-8.

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AbstractLet R be a commutative Noetherian ring, α an ideal of R and M a finitely generated R-module. Let t be a non-negative integer. It is known that if the local cohomology module is finitely generated for all i < t, then is finitely generated. In this paper it is shown that if is Artinian for all i < t, then need not be Artinian, but it has a finitely generated submodule N such that /N is Artinian.

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34

Rezaei, Sh. "General formal local cohomology modules." Algebra and Discrete Mathematics 30, no. 2 (2020): 254–66. http://dx.doi.org/10.12958/adm1068.

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Let (R,m) be a local ring, Φ a system of ideals of R and M a finitely generated R-module. In this paper, we define and study general formal local cohomology modules. We denote the ith general formal local cohomology module M with respect to Φ by FiΦ(M) and we investigate some finiteness and Artinianness properties of general formal local cohomology modules.

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35

Mafi, Amir, and Hossein Zakeri. "A Note on Local Cohomology." Algebra Colloquium 15, no. 01 (2008): 97–100. http://dx.doi.org/10.1142/s1005386708000096.

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A certain set of associated primes of the Matlis duality of any top local cohomology module of a complete filter local ring is characterized. Also, it is proved that the set of associated primes of a finitely generated module over a four-dimensional local ring is finite.

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36

Mafi, Amir. "On the Finiteness Results of the Generalized Local Cohomology Modules." Algebra Colloquium 16, no. 02 (2009): 325–32. http://dx.doi.org/10.1142/s1005386709000315.

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Let 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 [Formula: see text] is finite. Also, if the support of the local cohomology module [Formula: see text] is finite for all i < t, then the set [Formula: see text] is finite. Moreover, we prove that gdepth (𝔞+ Ann (M),N) is the least integer t such tha

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37

Roshan-Shekalgourabi, Hajar, and Dawood Hassanzadeh-Lelekaami. "On coLaskerian module and local cohomology." Communications in Algebra 47, no. 12 (2019): 5462–70. http://dx.doi.org/10.1080/00927872.2019.1631321.

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38

Aghapournahr, Moharram. "Weakly cofiniteness of local cohomology modules." Journal of Algebra and Its Applications 18, no. 05 (2019): 1950090. http://dx.doi.org/10.1142/s0219498819500907.

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Let [Formula: see text] be a commutative Noetherian ring, [Formula: see text] a system of ideals of [Formula: see text] and [Formula: see text]. Let [Formula: see text] be an [Formula: see text]-module (not necessary [Formula: see text]-torsion) such that [Formula: see text], then the [Formula: see text]-module [Formula: see text] is weakly Laskerian, for all [Formula: see text], if and only if the [Formula: see text]-module [Formula: see text] is weakly Laskerian for [Formula: see text]. Let [Formula: see text] be an integer and [Formula: see text] an [Formula: see text]-module such that [For

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39

Aghapournahr, Moharram, and Leif Melkersson. "Cofiniteness and coassociated primes of local cohomology modules." MATHEMATICA SCANDINAVICA 105, no. 2 (2009): 161. http://dx.doi.org/10.7146/math.scand.a-15112.

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Let $R$ be a noetherian ring, $\mathfrak a$ an ideal of $R$ such that $\dim R/{\mathfrak a}=1$ and $M$ a finite $R$-module. We will study cofiniteness and some other properties of the local cohomology modules $H^{i}_{{\mathfrak a}}(M)$. For an arbitrary ideal $\mathfrak a$ and an $R$-module $M$ (not necessarily finite), we will characterize $\mathfrak a$-cofinite artinian local cohomology modules. Certain sets of coassociated primes of top local cohomology modules over local rings are characterized.

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40

Dibaei, Mohammad T., and Siamak Yassemi. "Top Local Cohomology Modules." Algebra Colloquium 14, no. 02 (2007): 209–14. http://dx.doi.org/10.1142/s1005386707000211.

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For a finitely generated module M over a commutative Noetherian local ring (R,𝔪), it is shown that there exist only a finite number of non-isomorphic top local cohomology modules [Formula: see text] for all ideals 𝔞 of R. It is also shown that for a given integer r ≥ 0, if [Formula: see text] is zero for all 𝔭 in Supp (M), then [Formula: see text] for all i ≥ r.

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41

DIVAANI-AAZAR, K., and P. SCHENZEL. "Ideal topologies, local cohomology and connectedness." Mathematical Proceedings of the Cambridge Philosophical Society 131, no. 2 (2001): 211–26. http://dx.doi.org/10.1017/s0305004101005229.

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Let [afr ] be an ideal of a local ring (R, [mfr ]) and let N be a finitely generated R-module of dimension d: It is shown that Hd[afr ](N) ≃ Hd[mfr ](N)/[sum ]n∈ℕ〈[mfr ]〉 (0: Hd[mfr ](N)[afr ]n); where for an Artinian R-module X we put 〈[mfr ]〉X = ∩n∈ℕ[mfr ]nX. As a consequence several vanishing and connectedness results are deduced.

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42

Hamaali, Payman Mahmood, and Adil Kadir Jabbar. "On the primefulness of local cohomology modules." Samarra Journal of Pure and Applied Science 3, no. 1 (2021): 108–12. http://dx.doi.org/10.54153/sjpas.2021.v3i1.243.

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Let be a commutative Noetherian ring with identity For a non-zero module . We prove that a multiplication primeful module and are I-cofinite and primeful, for each where is an ideal of with . As a consequence, we deduce that, if and are multiplication primeful R- modules, then is primeful. Another result is, for a projective module over an integral domain, admits projective resolution such that each is primeful (faithfully flat).

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43

Bitoun, Thomas. "Length of Local Cohomology in Positive Characteristic and Ordinarity." International Mathematics Research Notices 2020, no. 7 (2018): 1921–32. http://dx.doi.org/10.1093/imrn/rny058.

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Abstract Let D be the ring of Grothendieck differential operators of the ring R of polynomials in d ≥ 3 variables with coefficients in a perfect field of characteristic p. We compute the D-module length of the 1st local cohomology module ${H^{1}_{f}}(R)$ with respect to a polynomial f with an isolated singularity, for p large enough. The expression we give is in terms of the Frobenius action on the top coherent cohomology of the exceptional fibre of a resolution of the singularity. Our proof rests on a tight closure computation of Hara. Since the above length is quite different from that of th

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44

Khashyarmanesh, K., and F. Khosh-Ahang. "A Note on the Artinianness and Vanishing of Local Cohomology and Generalized Local Cohomology Modules." Algebra Colloquium 16, no. 03 (2009): 517–24. http://dx.doi.org/10.1142/s1005386709000480.

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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. The second part is concerned with the vanishing of local cohomology and generalized local cohomology modules. In fact, when R is an arbitrary commutative Noetherian ring, M is an R-module and 𝔞 is an ideal of R, we obtain some lower and upper bounds for the

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45

Nam, Nguyen Thanh, Tran Tuan Nam, and Nguyen Minh Tri. "On cominimaxness of generalized local cohomology modules." Tạp chí Khoa học 16, no. 3 (2019): 50. http://dx.doi.org/10.54607/hcmue.js.16.3.2463(2019).

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This research introduces and focuses on (I, M)-cominimax modules. The paper shows that if t is an nonnegative integer, M is a finitely generated projective R-module and N is an R-module such that is minimax and is (I, M)-cominimax for all then is minimax and is finite.

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46

Asadollahi, J., K. Khashyarmanesh, and SH Salarian. "A generalization of the cofiniteness problem in local cohomology modules." Journal of the Australian Mathematical Society 75, no. 3 (2003): 313–24. http://dx.doi.org/10.1017/s1446788700008132.

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AbstractLetRbe a commutative Noetherian ring with nonzero identity and letMbe a finitely generated R-module. In this paper, we prove that if an idealIofRis generated by a u.s.d-sequence onMthen the local cohomology module(M) isI-cofinite. Furthermore, for any system of ideals Φ of R, we study the cofiniteness problem in the context of general local cohomology modules.

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47

Mafi, Amir. "Local Cohomology and Sequentially Cohen-Macaulay Modules." Algebra Colloquium 18, spec01 (2011): 815–18. http://dx.doi.org/10.1142/s1005386711000691.

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Let (R, 𝔪) be a commutative Noetherian local ring and N a finitely generated R-module with dim M =d. It is shown that M is a sequentially Cohen-Macaulay module if and only if the modules [Formula: see text] are either 0 or co-Cohen-Macaulay of Noetherian dimension i for all 0 ≤ i ≤ d.

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48

Huneke, Craig, and Jee Koh. "Cofiniteness and vanishing of local cohomology modules." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 3 (1991): 421–29. http://dx.doi.org/10.1017/s0305004100070493.

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Let R be a noetherian local ring with maximal ideal m and residue field k. If M is a finitely generated R-module then the local cohomology modules are known to be Artinian. Grothendieck [3], exposé 13, 1·2 made the following conjecture:If I is an ideal of R and M is a finitely generated R-module, then HomR (R/I, ) is finitely generated.

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Katzman, Mordechai, Linquan Ma, Ilya Smirnov, and Wenliang Zhang. "$D$-module and $F$-module length of local cohomology modules." Transactions of the American Mathematical Society 370, no. 12 (2018): 8551–80. http://dx.doi.org/10.1090/tran/7266.

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50

Bui, Cam Thi Hong, and Tri Minh Nguyen. "On the cominimaxness of generalized local cohomology modules." Science and Technology Development Journal 23, no. 1 (2020): 479–83. http://dx.doi.org/10.32508/stdj.v23i1.1696.

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Abstract:

The local cohomology theory plays an important role in commutative algebra and algebraic geometry. The I-cofiniteness of local cohomology modules is one of interesting properties which has been studied by many mathematicians. The I-cominimax modules is an extension of I-cofinite modules which was introduced by Hartshorne. An R-module M is I-cominimax if Supp_R(M)\subseteq V(I) and Ext^i_R(R/I,M) is minimax for all i\ge 0. In this paper, we show some conditions such that the generalized local cohomology module H^i_I(M,N) is I-cominimax for all i\ge 0. We show that if H^i_I(M,K) is I-cofinite fo

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